UNIVERSITY  OF  CALIFORNIA. 

FRO\\   THH    LIBRARY   Ol 

BENJAMIN  PARKE  AVERY. 


GIFT  OF  MRS.  AVERY, 

August,  1806. 

s  No. 


i    /- 

fj  iw     A-^u  .  V 


LIGHT  AND  ELECTRICITY: 


l^OTES 

OF 

TWO    COURSES    OF  LECTURES    BEFORE    THE  ROYAL 
INSTITUTION  OF  GREAT  BRITAIN. 


BY 

JOHN  TYNDALL,  LL.  D.,  F.  E.  S., 

AUTHOB  OP  "HEAT  AS  A  MODE  OF  MOTION,"  "LECTURES  ON  SOUND,"  "FRAGMENTS  OF 

SCIENCE  FOB  UNSCIENTIFIC  PEOPLE,11  "  HOURS  OF  EXEECISE  IN-  THE  ALPS," 

ETC.,  ETC.;  PROFESSOR  OF  NATURAL  PHILOSOPHY  IN  THE 

EOYAL  INSTITUTION   OF  GREAT   BRITAIN. 


NEW  YOEK: 
D.    APPLETON    AND    COMPANY, 

549     &     551     BROADWAY. 
1871. 


PREFACE  TO  THE  AMERICAN  EDITION. 


FOE  the  benefit  of  those  who  attended  his  lectures  on 
Light  and  Electricity  at  the  Royal  Institution,  Prof. 
Tyndall  prepared  with  much  care  a  series  of  Notes,  sum- 
ming up  briefly  and  clearly  the  leading  facts  and  princi- 
ples of  these  sciences.  The  Notes  proved  so  serviceable 
to  those  for  whom  they  were  designed,  that  they  were 
widely  sought  by  students  and  teachers,  and  Prof. 
Tyndall  accordingly  had  them  reprinted  in  two  small 
books.  Under  the  conviction  that  they  will  be  equally 
appreciated  by  instructors  and  .learners  in  this  country, 
they  are  here  combined  and  republished  in  a  single 
volume. 

No  intelligent  teacher  or  earnest  student  needs  to  be 
reminded  of  the  importance  of  repetition  and  recapitula- 
tion to  give  permanence  to  mental  impressions.  But  it  is 
neither  possible  nor  desirable  to  retain  in  the  memory 
the  copious  details  which  may  be  necessary  to  the  first 
comprehension  of  a  subject.  Hence,  after  listening  to 
a  course  of  lectures,  or  going  through  an  extended  work 
in  which  facts,  experimental  proofs,  and  speculations,  have 


4  PREFACE  TO   THE  AMERICAN  EDITION. 

been  elaborately  presented,  it  is  invaluable  to  retravcrsc 
the  field,  concentrating  attention  upon  the  prominent 
and  established  principles  of  the  subject.  This  is  an  in- 
dispensable condition  of  all  solid  acquisition ;  and,  in  thus 
clearly  and  sharply  stating  the  fundamental  principles  of 
Electrical  and  Optical  Science,  Prof.  Tyndall  has  earned 
the  cordial  thanks  of  all  interested  in  education. 

NEW  YORK,  April,  1871. 


CONTENTS. 


LIGHT. 

PAGE 

General  Considerations.     Eectilinear  Propagation  of  Light  .            .     11 

Formation  of  Images  through  Small  Apertures    .  .            .           12 

Shadows          .            .            .                         .            .  .            .13 

Enfeeblement  of  Light  by  Distance  :  Law  of  Inverse  Squares     .           15 

Photometry,  or  the  Measurement  of  Light    .            .  .            .16 

Brightness             .            .            .            .            .  .            .17 

Light  requires  Tune  to  pass  through  Space    .            .  .            .19 

Aberration  of  Light          .            .                         .  .            .20 

Reflection  of  Light  (Catoptrics) — Plane  Mirrors        .  .            .22 

Verification  of  the  Law  of  Reflection       .            .  .            .           22 

Reflection  from  Curved  Surfaces :  Concave  Mirrors   .  .            .27 

Caustics  by  Reflection  (Catacaustics)       .            .  .            .           31 

Convex  Mirrors           .            .            .            .            .  .            .32 

Refraction  of  Light  (Dioptrics)    .            .  33 

Opacity  of  Transparent  Mixtures       .            .            .  .            .39 

Total  Reflection    .            .            .            .            .  .            .41 

Lenses             .            .            .            .            .            .  .            .44 

Converging  Lenses            .            .            .            .  .            .44 

Diverging  Lenses        .            .            .            .            .  .            .44 

Vision  and  the  Eye           .            .            .            .  .            .46 

Adjustment  of  the  Eye  :  Use  of  Spectacles    .            .  .            .48 

The  Punctum  Co3cmn  50 


6  CONTENTS. 

PAGE 

Persistence  of  Impressions     .           .            .            .            .  .61 

Bodies  seen  within  the  Eye           .            .            .            .            .  52 

The  Stereoscope          .            .            .            .            .            .  .64 

Nature  of  Light ;  Physical  Theory  of  Reflection  and  Refraction  57 
Theory  of  Emission          .             .             .             .             .             .57 

s  Theory  of  Undulation             .             .             .             .             .  .59 

Prisms       ........  64 

Prismatic  Analysis  of  Light :  Dispersion       .            .            .  .65 

Invisible  Rays  :  Calorescence  and  Fluorescence  .            .            .  66 

Doctrine  of  Visual  Periods     .            .            .            .            .  .68 

Doctrine  of  Colors            ......  69 

Chromatic  Aberration.     Achromatism            .            .            .  .71 

Subjective  Colors .......  72 

Spectrum  Analysis      .            .            .            .            .            .  .74 

Further  Definition  of  Radiation  and  Absorption  ...  75 

The  pure  Spectrum :  Fraunhofer's  Lines        .            .            .  .77 

Reciprocity  of  Radiation  and  Absorption            .            .            .  78 

Solar  Chemistry           .             .             .             .             .             .  .80 

Planetary  Chemistry         .  .  .  .  .  .81 

Stellar  Chemistry         .             .             .             .             .             .  .82 

Nebular  Chemistry           ......  82 

The  Red  Prominences  and  Envelope  of  the  Sun         .            .  .82 

The  Rainbow        .......  84 

Interference  of  Light .            .            .            .            .            .  .86 

Diffraction,  or  the  Inflection  of  Light      .             .             .             .  88 

Measurement  of  the  Waves  of  Light .            .            .            .  .93 

Colors  of  Thin  Plates       .  .  .  .  .  .96 

Double  Refraction       .            .            .            .            .            .  .101 

Phenomena  presented  by  Iceland  Spar    .            .            .  '          .  104 

Polarization  of  Light               .             .             .             .             .  .106 

Polarization  of  Light  by  Reflection          ....  108 

Polarization  of  Light  by  Refraction  .            .            .            .  .110 

Polarization  of  Light  by  Double  Refraction         .  .  .110 


CONTENTS.  7 

PAGE 

Examination  of  Light  transmitted  through  Iceland  Spar        .  .111 

Colors  of  Double-refracting  Crystals  in  Polarized  Light  .  .         114 

Rings  surrounding  the  Axes  of  Crystals  in  Polarized  Light  .  ,119 

Elliptic  and  Circular  Polarization             .            .            .  .120 

Rotatory  Polarization              .            .            .            .            .  .121 

CONCLUSION  123 


ELECTRICITY. 

Voltaic  Electricity :  the  Voltaic  Battery  .  .  .          131 

Electro-Magnetism :  Elementary  Phenomena  .  .  .133 

Electro-Magnetic  Engines  .  .  .  .  .         135 

Physical  Effects  of  Magnetization       .  .  .  .  .136 

Character  of  Magnetic  Force        .  .  .  .  .138 

Magnetism  of  Helix  :  Strength  of  Electro-Magnets    .  .  .140 

Electro-Magnetic  Attractions :  Law  of  Squares  .  .  .         140 

Inference  from  Law  of  Squares ;  Theoretic  Notions  .  .  .  143 

Diamagnetism :  Magne-Crystallic  Action  .  .  .         144 

Frictional  Electricity:  Attraction  and  Repulsion:   Conduction  and 

Insulation         .......  145 

Theories  of  Electricity :  Electric  Fluids  .';"-.  .  .         147 

Electric  Induction :  the  Condenser :  the  Electrophorus          .  .  148 

The  Electric  Machine :  the  Leyden-jar     ....         149 

The  Electric  Current  .  .  .  .  .  .  .150 

The  Electric  Discharge :  Thunder  and  Lightning  .  .         151 

Electric  Density :  Action  of  Points    .....  152 

Relation  of  Voltaic  to  Frictional  Electricity        .  .  .         153 

Historic  Jottings,  concerning  Conduction  and  the  Leyden-jar  .  155 

Historic  Jottings,  concerning  the  Electric  Telegraph       .  .          156 

Phenomena  observed  in  Telegraph-Cables      ....  159 

Artificial  Cables    .......          163 

Sketch  of  Ohm's  Theory  and  Kohlrausch's  Verification        .  .165 


8  CONTENTS. 

PAGE 

Electro-chemistry.     Chemical  Actions  in  the  Voltaic  Cell :  Origin  of 

the  Current  ......         168 

Chemical  Actions  at  a  Distance :  Electrolysis  . .  .  .170 

Measures  of  the  Electric  Current  .  .  .  .174 

Electric  Polarization :  Ritter's  Secondary  Pile  .  .  .175 

Faraday's  Electrolytic  Law  .  .  .  .  .177 

Nobili's  Iris  Rings       .  .  .  .  .  .178 

Distribution  of  Heat  in  the  Circuit          .  .  .  .179 

Relation  of  Heat  to  Current  and  to  Resistance          .  .  .180 

Magneto-Electricity :  Induced  Currents   .  .  .  .          181 

Relation  of  Induced  Currents  to  the  Lines  of  Magnetic  Force.    Rota- 
tory Magnetism  .  .  .  .  .  .184 

The  Extra-Current  .  .  .  .  .186 

Influence  of  Time  on  Intensity  of  Discharge.     The  Condenser          .  187 
Electric  Discharge  through  rarefied  Gases  and  Vapors    .  .         188 

Action  of  Magnets  on  the  Luminous  Discharge          .  .  .190 

Magneto-electric  Machines.    Saxton's  Machine.    Siemens's  Armature  191 
Wilde's  Machine         .  .  .  .  .  .  .192 

Siemens's  and  Wheatstone's  Machine       .  .  .  .193 

Induced  Currents  of  the  Leyden-Battery       .  .  .  .  1 94 


NOTES 

OF  A  COURSE  OF  NINE  LECTURES  ON 

LIGHT. 


UHI7ERSIT7 


NOTES    ON    LIGHT. 


General  Considerations.     Rectilinear  Propagation  of 
Light. 

1.  THE  ancients  supposed  light  to  be  produced  and 
vision  excited  by  something  emitted  from  the  eye.     The 
moderns  hold  vision  to  be  excited  by  something  that 
strikes  the  eye  from  without.     What  that  something  is 
we  shall  consider  more  closely  subsequently. 

2.  Luminous  bodies  are  independent  sources  of  light. 
They  generate  it  and  emit  it,  and  do  not  receive  their 
light  from  other  bodies.     The  sun,  a  star,  a  candle-flame, 
are  examples. 

3.  Illuminated  bodies  are  such  as  receive  the  light  by 
which  they  are  seen  from  luminous  bodies.     A  house,  a 
tree,  a  man,  are  examples.     Such  bodies  scatter  in  all 
directions  the  light  which  they  receive  ;  this  light  reaches 
the  eye,  and  through  its  action  the  illuminated  bodies  are 
rendered  visible. 

4.  All  illuminated  bodies  scatter  or  reflect  light,  and 
they  are  distinguished  from  each  other  by  the  excess  or 
defect  of  light  which  they  send  to  the  eye.     A  white  cloud 
in  a  dark-blue  firmament  is  distinguished  by  its  excess  of 
light ;  a  dark  pine-tree  projected  against  the  same  cloud  is 
distinguished  through  its  defect  of  light. 

5.  Look  at  any  point  of  a  visible  object.     The  light 
comes  from  that  point  in  straight  lines  to  the  eye.     The 


12  NOTES  ON  LIGHT. 

lines  of  light,  or  rays  as  they  are  called,  that  reach  the 
pupil  form  a  cone,  with  the  pupil  for  a  base,  and  with  the 
point  for  an  apex.  The  point  is  always  seen  at  the  place 
where  the  rays  which  form  the  surface  of  this  cone  inter- 
sect each  other,  or,  as  we  shall  learn  immediately,  where 
they  seem  to  intersect  each  other. 

6.  Light,  it  has  just  been  said,  moves  in  straight  lines ; 
you  see  a  luminous  object  by  means  of  the  rays  which  it 
sends  to  the  eye,  but  you  cannot  see  round  a  corner.     A 
small  obstacle  that  intercepts  the  view  of  a  visible  point 
is  always  in  the  straight  line  between  the  eye  and  the 
point.     In  a  dark  room  let  a  small  hole  be  made  in  a  win- 
dow-shutter, and  let  the  sun  shine  through  the  hole.     A 
narrow  luminous  beam  will  mark  its  course  on  the  dust 
of  the  room,  and  the  track  of  the  beam  will  be  perfectly 
straight. 

7.  Imagine  the  aperture  to  diminish  in  size  until  the 
beam  passing  through  it  and  marking  itself  upon  the  dust 
of  the  room  shall  dwindle  to  a  mere  line  in  thickness.     In 
this  condition  the  beam  is  what  we  call  a  ray  of  light. 

Formation  of  Images  through  Small  Apertures. 

8.  Instead  of  permitting  the  direct  sunlight  to  enter 
the  room  by  the  small  aperture,  let  the  light  from  some 
body  illuminated  by  the  sun — a  tree,  a  house,  a  man,  for 
example — be  permitted  to  enter.     Let  this  light  be  re- 
ceived upon  a  white  screen  placed  in  the   dark  room. 
Every  visible  point  of  the  object  sends  a  straight  ray  of 
light  through  the  aperture.     The  ray  carries  with  it  the 
color  of  the  point  from  which  it  issues,  and  imprints  the 
color  upon  the  screen.     The  sum  total  of  the  rays  falling 
thus  upon  the  screen  produces  an  inverted  image  of  that 
object.     The  image  is  inverted  because  the  rays  cross  each 
other  at  the  aperture. 


SHADOWS.  13 

9.  Experimental  Illustration. — Place  a  lighted  candle 
in  a  small  camera  with  a  small  orifice  in  one  of  its  sides, 
or  a  large  one  covered  by  tin-foil.     Prick  the  tin-foil  with 
a  needle ;  the  inverted  image  of  the  flame  will  immediate- 
ly appear  upon  a  screen  placed  to  receive  it.     By  ap- 
proaching the  camera  to  the  screen,  or  the  screen  to  the 
camera,  the  size  of  the  image  is  diminished ;  by  augment- 
ing the  distance  between  them,  the  size  of  the  image  is 
increased. 

10.  The  boundary  of  the  image  is  formed  by  drawing 
from  every  point  of  the  outline  of  the  object  straight  lines 
through  the  aperture,  and  producing  these  lines  until  they 
cut  the  screen.     This  could  not  be  the  case  if  the  straight 
lines  and  the  light  rays  were  not  coincident. 

11.  Some  bodies  have  the  power  of  permitting  light  to 
pass  freely  through  them;  they  are  transparent  bodies. 
Others  have  the  power  of  rapidly  quenching  the  light  that 
enters  them ;  they  are  opaque  bodies.     There  is  no  such 
thing  as  perfect  transparency  or  perfect  opacity.     The 
purest  glass  and  crystal  quench   some  rays;    the  most 
opaque  metal,  if  thin  enough,  permits  some  rays  to  pass 
through  it.     The  redness  of  the  London  sun  in  smoky 
weather  is  due  to  the  partial  transparency  of  soot  for  the 
red  light.     Pure  water  at  great  depths  is  blue;  it  quenches 
more  or  less  the  red  rays.     Ice  when  seen  in  large  masses 
in  the  glaciers  of  the  Alps  is  blue  also. 

Shadows. 

12.  As  a  consequence  of  the  rectilinear  motion  of  light, 
opaque  bodies  cast  shadows.     If  the  source  of  light  be  a 
point,  the  shadow  is  sharply  defined;  if  the  source  be 
a  luminous  surface,  the  perfect  shadow  is  fringed  by  aft 
imperfect  shadow  called  a  penumbra. 

13.  When  light  emanates  from  a  point,  the  shadow  of 


14  NOTES  ON  LIGHT. 

a  sphere  placed  in  the  light  is  a  divergent  cone  sharply 
defined. 

14.  When  light  emanates  from  a  luminous  globe,  the 
perfect  shadow  of  a  sphere  equal  to  the  globe  in  size  will 
be  a  cylinder  •  it  will  be  bordered  by  a  penumbra. 

15.  If  the  luminous  sphere  l>e  the  larger  of  the  two, 
the  perfect  shadow  will  be  a  convergent  cone  /  it  will  be 
surrounded  by  a  penumbra.     This  is  the  character  of  the 
shadows  cast  by  the  earth  and  moon  in  space ;  for  the  sun 
is  a  sphere  larger  than  either  the  earth  or  the  moon. 

16.  To  an  eye  placed  in  the  true  conical  shadow  of  the 
moon,  the  sun  is  totally  eclipsed ;  to  an  eye  in  the  penum- 
bra, the  sun  appears  horned ;  while  to  an  eye  placed  be- 
yond the  apex  of  the  conical  shadow  and  within  the  space 
enclosed  by  the  surface  of  the  cone  produced,  the  eclipse 
is  annular.    All  these  eclipses  are  actually  seen  from  time 
to  time  from  the  earth's  surface. 

17.  The  influence  of  magnitude  may  be  experimentally 
illustrated  by  means  of  a  bat's-wing  or  fish-tail  flame ;  or 
by  a  flat  oil  or  paraffine  flame.     Holding  an  opaque  rod 
between  the  flame  and  a  white  screen,  the  shadow  is  sharp 
when  the  edge  of  the  flame  is  turned  toward  the  rod. 
When  the  broad  surface  of  the  flame  is  pointed  to  the 
rod,  the  real  shadow  is  fringed  by  a  penumbra. 

18.  As  the   distance  from  the  screen  increases,  the 
penumbra  encroaches  more  and  more  upon  the  perfect 
shadow,  and  finally  obliterates  it. 

19.  It  is  the  angular  magnitude  of  the  sun  that  de- 
stroys the  sharpness  of  solar  shadows.     In  sunlight,  for 
example,  the  shadow  of  a  hair  is  sensibly  washed  away  at 
a  few  inches  distance  from  the  surface  on  which  it  falls. 
The  electric  light,  on  the  contrary,  emanating  as  it  does 
from  small  carbon  points,  casts  a  defined  shadow  of  a  hair 
upon  a  screen  many  feet  distant. 


• 

ENFEEBLEMENT  OF  LIGHT  BY  DISTANCE.  15 

Enfeeblement  of  Light  Tyy  Distance  /   Law   of  Inverse 
Squares. 

20.  Light  diminishes  in  intensity  as  we  recede  from 
the  source  of  light.     If  the  luminous  source  be  a  point, 
the  intensity  diminishes  as  the  square  of  the  distance  in- 
creases.   Calling  the  quantity  of  light  falling  upon  a  given 
surface  at  the  distance  of  a  foot  or  a  yard — 1,  the  quantity 
falling  on  it  at  a  distance  of  2  feet  or  2  yards  is  |-,  at  a 
distance  of  3  feet  or  3  yards  it  is  {-,  at  a  distance  of  10  feet 
or  10  yards  it  would  be  yj^,  and  so  on.    This  is  the  mean- 
ing of  the  law  of  inverse  squares  as  applied  to  light. 

21.  Experimental  Illustrations. — Place  your  source  of 
light,  which  may  be  a  candle-flame — though  the  law  is  in 
strictness  true  only  for  points — at  a  distance  say  of  9  feet 
from  a  white  screen.     Hold  a  square  of  pasteboard,  or 
some  other  suitable  material,  at  a  distance  of  2£  feet  from 
the  flame,  or  £th  of  the  distance  of  the  screen.    The  square 
casts  a  shadow  upon  the  screen. 

22.  Assure  yourself  that  the  area  of  this  shadow  is 
sixteen  times  that  of  the  square  which  casts  it ;  a  student 
of  Euclid  will  see  in  a  moment  that  this  must  be  the  case, 
and  those  who  are  not  geometers  can  readily  satisfy  them- 
selves  by  actual  measurement.     Dividing,  for  example, 
each  side  of  a  square  sheet  of  paper  into  four  equal  parts, 
and  folding  the  sheet  at  the  opposite  points  of  division,  a 
small  square  is  obtained  y^-th  of  the  area  of  the  large  one. 
Let  this  small  square,  or  one  equal  to  it,  be  your  shadow- 
casting  body.     Held  at  2J  feet  from  the  flame,  its  shadow 
upon  the  screen  9  feet  distant  will  be  exactly  covered  by 
the  entire  sheet  of  paper.     "Wlien,  therefore,  the  small 
square  is  removed,  the  light  that  fell  upon  it  is  diffused 
over  sixteen  times  the  area  on  the  screen;  it  is  therefore 
diluted  to  y^th  of  its  former  intensity.     That  is  to  say,  by 


16  NOTES  ON  LIGHT. 

augmenting  the  distance  fourfold  we  diminish  tLe  light 
sixteenfold. 

23.  Make  the  same  experiment  by  placing  a  square  at 
a  distance  of  3  feet  from  the  source  of  light  and  6  from 
the  screen.     The  shadow  now  cast  by  the  square  will  have 
nine  times  the  area  of  the  square  itself ;  hence  the  light 
falling  on  the  square  is  diffused  over  nine  times  the  surface 
upon  the  screen.     It  is,  therefore,  reduced  to  ^th  of  its 
intensity.     That  is  to  say,  by  trebling  the  distance  from 
the  source  of  light  we  diminish  the  light  ninefold. 

24.  Make  the  same  experiment  at  a  distance  of  4J  fcet 
from  the  source.     The  shadow  here  will  be  four  times  the 
area  of  the  shadow-casting  square,  and  the  light  diffused 
over  the   greater  square  will  be  reduced  to  Jth  of  its 
former  intensity.     Thus,  by  doubling  the  distance  from 
the  source  of  light  we  reduce  the  intensity  of  the  light 
fourfold. 

25.  Instead  of  beginning  with  a  distance  of  2£  feet 
from  the  source,  we  might  have  begun  with  a  distance  of 
1  foot.     The  area  of  the  shadow  in  this  case  would  be 
eighty-one  times  that  of  the  square  which  casts  it ;  prov- 
ing that  at  9  feet  distance  the  intensity  of  the  light  is  -^ 
of  what  it  is  at  1  foot  distance. 

26.  Thus  when  the  distances  are 

1,     2,     3,     4,     5,     6,     V,     8,     9,    etc., 
the  relative  intensities  are 

1>    i,    l>    Ty»    A>    &,t  A>    -fa,    -fa,    etc. 
This  is  the  numerical  expression  of  the  law  of  inverse 
squares. 

Photometry,  or  the  Measurement  of  Light. 

27.  The  law  just  established  enables  us  to  compare 
one  light  with  another,  and  to  express  by  numbers  their 
relative  illuminating  powers. 


BRIGHTNESS.  17 

28.  The  more  intense  a  light,  the  darker  is  the  shadow 
which  it  casts ;  in  other  words,  the  greater  is  the  contrast 
between  the  illuminated  and  unilluminated  surface. 

29.  Place  an  upright  rod  in  front  of  a  white  screen  and 
a  candle-flame  at  some  distance  behind  the  rod,  the  rod 
casts  a  shadow  upon  the  screen. 

30.  Place  a  second  flame  by  the  side  of  the  first,  a 
second  shadow  is  cast,  and  it  is  easy  to  arrange  matters 
so  that  the  shadows  shall  be  close  to  each  other,  thus 
offering  themselves  for  easy  comparison  to  the  eye.     If 
when  the  lights  are  at  the  same  distance  from  the  screen 
the  two  shadows  are  equally  dark,  then  the  two  lights 
have  the  same  illuminating  power. 

31.  But  if  one  of  the  shadows  be  darker  than  the  other, 
it  is  because  its  corresponding  light  is  brighter  than  the 
other.    Remove  the  brighter  light  farther  from  the  screen, 
the  shadows  gradually  approximate  in  depth,  and  at  length 
the  eye  can  perceive  no  difference  between  them.     The 
shadow  corresponding  to  each  light  is  now  illuminated 
by  the  other  light,  and  if  the  shadows  are  equal  it  is  be- 
cause the  quantities  of  light  cast  by  both  upon  the  screen 
are  equal. 

32.  Measure  the  distances  of  the  two  lights  from  the 
screen,  and  square  these  distances.     The  two  squares  will 
express  the  relative  illuminating  powers  of  the  two  lights. 
Supposing  one  distance  to  be  3  feet  and  the  other  5,  the 
relative  illuminating  powers  are  as  9  to  25- 

Brightness. 

33.  But  if  light  diminishes  so  rapidly  with  the  distance 
—if,  for  example,  the  light  of  a  candle  at  the  distance  of  a 
yard  is  100  times  more  intense  than  at  the  distance  of  10 
yards — how  is  it  that  on  looking  at  lights  in  churches  or 
theatres,  or  in  large  rooms,  or  at  our  street-lamps,  a  light 


18  NOTES  ON   LIGHT. 

10  yards  off  appears  almost,  if  not  quite,  as  bright  as  one 
close  at  hand  ? 

34.  To  answer  this  question  I  must  anticipate  matters 
so  far  as  to  say  that  at  the  back  of  the  eye  is  a  screen, 
woven  of  nerve-filaments,  named  the  retina;    and  that 
when  we  see  a  light  distinctly,  its  image  is  formed  upon 
this  screen.     This  point  will  be  fully  developed  when  we 
come  to  treat  of  the  eye.     ISTow  the  sense  of  external 
brightness  depends  upon  the  brightness  of  this  internal 
retinal  image,  and  not  upon  its  size.     As  we  retreat  from 
a  light,  its  image  upon  the  retina  becomes  smaller,  and  it 
is  easy  to  prove  that  the  diminution  follows  the  law  of 
inverse  squares ;  that  at  a  double  distance  the  area  of 
the  retinal  image  is  reduced  to  one-fourth,  at  a  treble  dis- 
tance to  one-ninth,  and  so  on.     The  concentration  of  light 
accompanying  this  decrease  of  magnitude  exactly  atones 
for  the  diminution  due  to  distance ;  hence,  if  the  air  be 
clear,  the  light,  within  wide  variations  of  distance,  appears 
equally  bright  to  the  observer. 

35.  If  an  eye  could  be  placed  behind  the  retina,  the 
augmentation  or  diminution  of  the  image,  with  the  de- 
crease or  increase  of  distance,  might  be  actually  observed. 
An  exceedingly  simple  apparatus  enables  us  to  illustrate 
this  point.     Take  a  pasteboard  or  tin  tube,  three  or  four 
inches  wide   and  three  or  four  inches  long,  and  cover 
one  end  of  it  with  a  sheet  of  tin-foil,  and  the  other  with 
tracing-paper,   or  ordinary  letter-paper  wetted  with   oil 
or  turpentine.      Prick  the   tin-foil  with  a  needle,   and 
turn  the  aperture  toward  a  candle-flame.     An  inverted 
image  of  the  flame  will  be  seen  on  the  translucent  paper 
screen  by  the  eye  behind  it.     As  you  approach  the  flame 
the  image  becomes  larger,  as  you  recede  from  the  flame  the 
image  becomes  smaller ;  but  the  brightness  remains  through- 
out the  same.     It  is  so  with  the  image  upon  the  retina. 


LIGHT  REQUIRES  TIME  TO   PASS  THROUGH  SPACE.    19 

36.  If  a  sunbeam  be  permitted  to  enter  a  room  through 
a  small  aperture,  the  spot  of  light  formed  on  a  distant 
screen  will  be  round,  whatever  be  the  shape  of  the  aper- 
ture ;  this  curious  effect  is  due  to  the  angular  magnitude 
of  the  sun.    Were  the  sun  a  point,  the  light  spot  would  be 
accurately  of  the  same  shape  as  the  aperture.     Supposing, 
then,  the  aperture  to  be  square,  every  point  of  light  round 
the  sun's  periphery  sends  a  small  square  to  the  screen. 
These  small  squares  are  ranged  round  a  circle  correspond- 
ing to  the  periphery  of  the  sun ;  through  their  blending 
and  overlapping  they  produce  a  rounded  outline.     The 
spots  of  light  which  fall  through  the  apertures  of  a  tree's 
foliage  on  the  ground  are  rounded  for  the  same  reason. 

Light  requires  Time  to  pass  through  Space. 

37.  This  was  proved  in  1675  and  1676  by  an  eminent 
Dane,  named  Olaf  Koemer,  who  was  then  engaged  with 
Cassini  in  Paris  in  observing  the   eclipses  of  Jupiter's 
moons.     The  planet,  whose  distance  from  the  sun  is  475,- 
693,000  miles,  has  four  satellites.     We  are  now  only  con- 
cerned with  the  one  nearest  to  the  planet.    Rcemer  watched 
this  moon,  saw  it  move  round  in  front  of  the  planet,  pass 
to  the  other  side  of  it,  and  then  plunge  into  Jupiter's 
shadow,  behaving  like  a  lamp  suddenly  extinguished :  at 
the  other  edge  of  the  shadow  he  saw  it  reappear  like  a 
lamp  suddenly  lighted.     The  moon  thus  acted  the  part  of 
a  signal-light  to  the  astronomer,  which  enabled  him  to 
tell  exactly  its  time  of  revolution.     The  period  between 
two  successive  lightings  up  of  the  lunar  lamp  gave  this 
time.     It  was  found  to  be  42  hours,  28  minutes,  and  35 
seconds. 

38.  This  observation  was  so  accurate,  that  having  de- 
termined the  moment  when  the  moon  emerged  from  the 
shadow,  the  moment  of  its  hundredth  appearance  could 


2Q  NOTES  ON  LIGHT. 

also  be  determined.  In  fact,  it  would  be  100  times  42 
hours,  28  minutes,  35  seconds,  from  the  first  observa- 
tion. 

39.  Rcemer's   first   observation  was   made  when  the 
earth  was  in  the  part  of  its  orbit  nearest  Jupiter.     About 
six  months  afterward,  when  the  little  moon  ought  to  make 
its  appearance  for  the  hundredth  time,  it  was  found  un- 
punctual,  being  fully  15  minutes  behind  its   calculated 
time.     Its  appearance,  moreover,  had  been  growing  grad- 
ually later,  as  the  earth  retreated  toward  the  part  of  its 
orbit  most  distant  from  Jupiter. 

40.  Roemer  reasoned  thus:  "Had  I  been  able  to  re- 
main at  the  other  side  of  the  earth's  orbit,  the  moon  might 
have  appeared  always  at  the  proper  instant ;  an  observer 
placed  there  would   probably  have   seen  the  moon   15 
minutes  ago,  the  retardation  in  my  case   being  due  to 
the  fact  that  the  light  requires  15  minutes  to  travel  from 
the  place  where  my  first  observation  was  made  to  my 
present  position." 

41.  This  flash  of  genius  was  immediately  succeeded  by 
another.     "  If  this  surmise  be  correct,"  Rremer  reasoned, 
"  then  as  I  approach  Jupiter  along  the  other  side  of  the 
earth's  orbit,  the  retardation  ought  to  become  gradually 
less,  and  when  I  reach  the  place  of  my  first  observation 
there  ought  to  be  no  retardation  at  all."     He  found  this 
to  be  the  case,  and  thus  proved  not  only  that  light  re- 
quired time  to  pass  through  space,  but  also  determined 
its  rate  of  propagation. 

42.  The  velocity  of  light  as  determined  by  Roemer  is 
192,500  miles  in  a  second. 

The  Aberration  of  Light. 

The  astounding  velocity  assigned  to  light  by  the  ob- 
servations of  Roamer  received  the  most  striking  confirma- 


THE  ABERRATION  OF  LIGHT.  21 

tion  from  the  English  astronomer  Bradley  in  the  year 
1723.  In  Kew  Gardens  to  the  present  hour  there  is  a 
sundial  to  mark  the  spot  where  Bradley  discovered  the 
aberration  of  light. 

43.  If  we  move  quickly  through  a  rain-shower  which 
falls  vertically  downward,  the  drops  will  no  longer  seem 
to  fall  vertically,  but  will  appear  to  meet  us.     A  similar 
deflection  of  the  stellar  rays  by  the  motion  of  the  earth  in 
its  orbit  is  called  the  aberration  of  light. 

44.  Knowing  the  speed  at  which  we  move  through  a 
vertical  rain-shower,  and  knowing  the  angle  at  which  the 
rain-drops  appear  to  descend,  we  can  readily  calculate  the 
velocity  of  the  falling  drops  of  rain.     So,  likewise,  know- 
ing the  velocity  of  the  earth  in  its  orbit,  and  the  deflec- 
tion of  the  rays  of  light  produced  by  the  earth's  motion, 
we  can  immediately  calculate  the  velocity  of  light. 

45.  The  velocity  of  light,  as  determined  by  Bradley,  is 
191,515  miles  per  second — a  most  striking  agreement  with 
the  result  of  Rcemer. 

46.  This  velocity  has  also  been  determined  by  experi- 
ments over  terrestrial  distances.     M.  Fizeau  found  it  thus 
to  be  194,677  miles  a  second,  while  the  later  experiments 
of  M.  Foucault  made  it  185,177  miles  a  second. 

47.  "A  cannon-ball,"  says  Sir  John  Herschel,  "would 
require  seventeen  years  to  reach  the  sun,  yet  light  travels 
over  the  same  space  in  eight  minutes.     The  swiftest  bird, 
at  its  utmost  speed,  would  require  nearly  three  weeks  to 
make  the  tour  of  the  earth.     Light  performs  the  same  dis- 
tance in  much  less  time  than  is  necessary  for  a  single 
stroke  of  its  wing ;  yet  its  rapidity  is  but  commensurate 
with  the  distance  it  has  to  travel.     It  is   demonstrable 
that  light  cannot  reach  our  system  from  the  nearest  of  the 
fixed  stars  in  less  than  five  years,  and  telescopes  disclose 
to  us  objects  probably  many  times  more  remote." 


22  NOTES  ON  LIGHT. 

The  Reflection  of  Light  (Catoptrics) — Plane  Mirrors. 

48.  When  light  passes  from  one  optical  medium  to  an- 
other, a  portion  of  it  is  always  turned  back  or  reflected. 

49.  Light  is  regularly  reflected  by  a  polished  surface ; 
but  if  the  surface  be  not  polished,  the  light  is  irregularly 
reflected  or  scattered. 

50.  Thus  a  piece  of  ordinary  drawing-paper  will  scat- 
ter a  beam  of  light  that  falls  upon  it  so  as  to  illuminate  a 
room.     A  plane  mirror  receiving  the  sunbeam  will  reflect 
it  "in  a  definite  direction,  and  illuminate  intensely  a  small 
portion  of  the  room. 

51.  If  the  polish  of  the  mirror  were  perfect  it  would 
be  invisible,  we  should  simply  see  in  it  the  images  of  other 
objects ;    if  the  room  were  without   dust-particles,   the 
beam  passing  through  the  air  would  also  be  invisible.     It 
is  the  light  scattered  by  the  mirror  and  by  the  particles 
suspended  in  the  air  which  renders  them  visible. 

52.  A  ray  of  light  striking  as  a  perpendicular  against 
a  reflecting  surface  is  reflected  back  along  the  perpen- 
dicular ;  it  simply  retraces  its  own  course.     If  it  strike 
the  surface  obliquely,  it  is  reflected  obliquely. 

53.  Draw  a  perpendicular  to  the  surface  at  the  point 
where  the  ray  strikes  it ;  the  angle  enclosed  between  the 
direct  ray  and  this  perpendicular  is  called  the  angle  of  in- 
cidence.    The  angle  enclosed  by  the  reflected  ray  and  the 
perpendicular  is  called  the  angle  of  reflection. 

54.  It  is  a  fundamental  law  of  optics  that  the  angle  of 
incidence  is  equal  to  the  angle  of  reflection. 

Verification  of  the  Law  of  Reflection. 

55.  Fill  a  basin  with  water  to  the  brim,  the  water  be- 
ing blackened  by  a  little  ink.     Let  a  small  -plummet — 
a  small  lead  bullet,  for  example — suspended  by  a  thread, 


VERIFICATION  OF  THE   LAW   OF   REFLECTION.         23 

hang  into  the  water.  The  water  is  to  be  our  horizontal 
mirror,  and  the  plumb-line  our  perpendicular.  Let  the 
plummet  hang  from  the  centre  of  a  horizontal  scale,  with 
inches  marked  upon  it  right  and  left  from  the  point  of 
suspension,  which  is  to  be  the  zero  of  the  scale.  A  lighted 
candle  is  to  be  placed  on  one  side  of  the  plumb-line,  the 
observer's  eye  being  at  the  other. 

56.  The  question  to  be  solved  is  this :  How  is  the  ray 
which  strikes  the  liquid  surface  at  the  foot  of  the  plumb- 
line  reflected  ?    Moving  the  candle  along  the  scale,  so  that 
the  tip  of  its  flame  shall  stand  opposite  different  numbers, 
it  is  found  that,  to  see  the  reflected  tip  of  the  flame  in  the 
direction  of  the  foot  of  the  plumb-line,  the  line  of  vision 
must  cut  the  scale  as  far  on  the  one  side  of  that  line  as  the 
candle  is  on  the  other.     In  other  words,  the  ray  reflect- 
ed  from  the  foot   of  the   perpendicular  cuts  the  scale 
accurately  at   the   candle's   distance   on  the   other  side 
of  the  perpendicular.     From  this  it  immediately  follows 
that  the  angle  of  incidence  is  equal  to  the  angle  of  reflec- 
tion. 

57.  With  an  artificial  horizon  of  this  kind,  and  employ- 
ing a  theodolite  to  take  the  necessary  angles,  the  law  has 
been  established  with  the  most  rigid  accuracy.   The  angle 
of  elevation  to  a  star  being  taken  by  the  instrument,  the 
telescope  is  then  pointed  downward  to  the  image  of  the 
star  reflected  from  the   artificial  horizon.     It  is   always 
found  that  the  direct  and  reflected  rays   enclose  equal 
angles  with  the  horizontal  axis  of  the  telescope,  the  reflected 
ray  being  as  far  below  the  horizontal  axis  as  the  direct  ray 
is  above  it.     On  account  of  the  star's  distance  the  ray 
which  strikes  the  reflecting  surface  is  parallel  with  the  ray 
which  reaches  the  telescope  directly,  and  from  this  follows, 
by  a  brief  }mt  rigid  demonstration,  the  law  above  enun- 
ciated. 


24  NOTES  ON   LIGHT. 

58.  The  path  described  by  the  direct  and  reflected  rays 
is  the  shortest  possible. 

59.  When  the  reflecting  surface  is  roughened,  rays  from 
different  points,  more  or  less  distant  from  each  other,  reach 
the  eye.    Thus,  a  breeze  crisping  the  surface  of  the  Thames 
or  Serpentine  sends  to  the  eye,  instead  of  single  images 
of  the  lamps  upon  their  margin,  pillars  of  light.     Blowing 
upon  our  basin  of  water,  we  also  convert  the  reflected  light 
of  our  candle  into  a  luminous  column. 

60.  Light  is  reflected  with  different  energy  by  different 
substances.    At  a  perpendicular  incidence,  only  18  rays  out 
of -every  1,000  are  reflected  by  water,  25  rays  per  1,000  by 
glass,  while  666  per  1,000  are  reflected  by  mercury. 

61.  When  the  rays  strike  obliquely,  a  greater  amount 
of  light  than  that  stated  in  60,  is  reflected  by  water  and 
glass.   Thus,  at  an  incidence  of  40°,  water  reflects  22  rays ; 
at  60°,  65  rays ;  at  80°,  333  rays ;  and  at  89j°  (almost 
grazing  the  surface),  it  reflects  721  rays  out  of  every  1,000. 
This  is  as  much  as  mercury  reflects  at  the  same  incidence. 

62.  The  augmentation  of  the   light  reflected   as  the 
obliquity  of  incidence  is  increased  may  be  illustrated  by 
our  basin  of  water.     Hold  the  candle  so  that  its  rays  en- 
close a  large  angle  with  the  liquid  surface,  and  notice  the 
brightness  of  its  image.     Lower  both  the  candle  and  the 
eye  until  the  direct  and  reflected  rays  as  nearly  as  possible 
graze  the  liquid  surface ;  the  image  of  the  flame  is  now 
much  brighter  than  before. 

Reflection  from  Looking-glasses. — Various  instructive 
experiments  with  a  looking-glass  may  be  here  performed 
and  understood. 

63.  Note  first  when  a  candle  is  placed  between  the  glass 
and  the  eye,  so  that  a  line  from  the  eye  through  the  candle 
is  perpendicular  to  the  glass,  that  one  well-denned  image 
of  the  candle  only  is  seen. 


VERIFICATION   OF  THE  LAW  OF  REFLECTION.        25 

G4.  Let  the  eye  now  be  moved  so  as  to  receive  an  ob- 
lique reflection ;  the  image  is  no  longer  single,  a  series  of 
images  at  first  partially  overlapping  each  other  being  seen. 
By  rendering  the  incidence  sufficiently  oblique  these 
images,  if  the  glass  be  sufficiently  thick,  may  be  completely 
separated  from  each  other. 

65.  The  first  image  of  the  series  arises  from  the  reflection 
of  the  light  from  the  anterior  surface  of  the  glass. 

66.  The  second  image,  which  is  usually  much  the  bright- 
est, arises  from  reflection  at  the  silvered  surface  of  the  glass. 
At  large  incidences,  as  we  have  just  learned,  metallic  re- 
flection far  transcends  that  from  glass. 

67.  The  other  images  of  the  series  are  produced  by  the 
reverberation  of  the  light. from  surface  to  surface  of  the 
glass.   At  every  return  from  the  silvered  surface  a  portion 
of  the  light  quits  the  glass  and  reaches  the  eye,  forming 
an  image  ;  a  portion  is  also  sent  back  to  the  silvered  sur- 
face, where  it  is  again  reflected.     Part  of  this  reflected 
beam  also  reaches  the  eye  and  yields  another  image.   This 
process  continues  :  the  quantity  of  light  reaching  the  eye 
growing  gradually  less,  and,  as  a  consequence,  the  succes- 
sive images  growing  dimmer,  until  finally  they  become  too 
dim  to  be  visible. 

68.  A  very  instructive  experiment  illustrative  of  the 
augmentation  of  the  reflection  from  glass,  through  aug- 
mented obliquity,  may  here  be  made.     Causing  the  candle 
and  the  eye  to  approach  the  looking-glass,  the  first  image 
becomes  gradually  brighter ;  and  you  end  by  rendering 
the  image  reflected  from  the  glass  brighter,  more  lumi- 
nous, than  that  reflected  from  the  metal.    Irregularities  in 
the  reflection  from  looking-glasses  often  show  themselves ; 
but  with  a  good  glass — and  there  are  few  glasses  so  de- 
fective as  not  to  possess,  at  all  events,  some  good  portions 
— the  succession  of  images  is  that  here  indicated. 

2 


26  NOTES  ON  LIGHT. 

69.  Position  and  Character  of  Images  in  Plane  Mir- 
rors.— The  image  in  a  plane  mirror  appears  as  far  behind 
the  mirror  as  the  object  is  in  front  of  it.     This  follows  im- 
mediately from  the  law  which  announces  the  equality  of 
the  angles  of  incidence  and  reflection.     Draw  a  line  repre- 
senting the  section  of  a  plane  mirror  ;  place  a  point  in  front 
of  it.     Rays  issue  from  that  point,  are  reflected  from  the 
mirror,  and  strike  the  pupil  of  the  eye.     The  pupil  is  the 
base  of  a  cone  of  such  rays.     Produce  the  rays  backward ; 
they  will  intersect  behind  the  mirror,  and  the  point  will 
be  seen  as  if  it  existed  at  the  place  of  intersection.     The 
place  of  intersection  is  easily  proved  to  be  as  far  behind 
the  mirror  as  the  point  is  in  front  of  it. 

70.  Exercises  in  determining  the  positions  of  images  in 
a  plane  mirror,  the  positions  of  the  objects  being  given, 
are  here  desirable.     The  image  is  always  found  by  simply 
letting  fall  a  perpendicular  from  each  point  of  the  object, 
and  producing  it  behind  the  mirror,  so  as  to  make  the  part 
behind  equal  to  the  part  in  front.     We  thus  learn  that  the 
image  is  of  the  same  size  and  shape  as  the  object,  agreeing 
with  it  in  all  respects  save  one — the  image  is  a  lateral  in- 
version of  the  object. 

71.  This  inversion  enables  us,  by  means  of  a  mirror,  to 
read  writing  written  backward,  as  if  it  were  written  in  the 
usual  way.     Compositors  arrange  their  type  in  this  back- 
ward fashion,  the  type  being  reversed  by  the  process  of 
printing.     A  looking-glass  enables  us  to  read  the  type  as 
the  printed  page. 

72.  Lateral  inversion  comes  into  play  when  we  look  at 
our  own  faces  in  a  glass.     The  right  cheek  of  the  object, 
for  example,  is  the  left  cheek  of  the  image ;  the  right  hand 
of  the  object  the  left  hand  of  the  image,  etc.     The  hair 
parted  on  the  left  in  the  object  is  seen  parted  to  the  right 
of  the  image,  etc. 


REFLECTION   FROM   CURVED   SURFACES.  27 

73.  A  plane  mirror  half  the  height  of  an  object  gives 
an  image  which  embraces  the  whole  height.    This  is  readily 
deduced  from  what  has  gone  before. 

74.  If  a  plane  mirror  be  caused  to  move  parallel  with 
itself,  the  motion  of  an  image  in  the  mirror  moves  with 
twice  its  rapidity. 

75.  The  same  is  true  of  a  rotating  mirror:   when  a 
plane  mirror  is  caused  to  rotate,  the  angle  described  by 
the  image  is  twice  that  described  by  the  mirror. 

76.  In  a  mirror  inclined  at  an  angle  of  45  degrees  to 
the  horizon,  the  image  of  an  erect  object  appears  hori- 
zontal, while  the  image  of   a  horizontal  object  appears 
erect. 

77.  An  object  placed  between  two  mirrors  enclosing 
an  angle  yields  a  number  of  images  depending  upon  the 
angle  enclosed  by  the  mirrors.     The  smaller  the  angle,  the 
greater  is  the  number  of  images.     To  find  the  number  of 
images,  divide  360°  by  the  number  of  degrees  in  the  angle 
enclosed  by  the  two   mirrors,  the  quotient,  if  a  whole 
number,  will  be  the  number  of  images,  plus  one,  or  it  will 
include  the  images  and  the  object.     The  construction  of 
the  kaleidoscope  depends  on  this. 

78.  When  the  angle  becomes  0 — in  other  words,  when 
the  mirrors  are  parallel — the  number  of  images  is  infinite. 
Practically,  however,  we  see  between  parallel  mirrors  a 
long  succession  of  images,  which  become  gradually  feebler, 
and  finally  cease  to  be  sensible  to  the  eye. 

Reflection  from  Curved  Surf  aces :  Concave  Mirrors. 

79.  It  has  been  already  stated  and  illustrated  that  light 
moves  in  straight  lines,  which  receive  the  name  of  rays. 
Such  rays  may  be  either  divergent,  parallel,  or  convergent. 

80.  Rays  issuing  from  terrestrial  points  are  necessarily 
divergent.   Rays  from  the  sun  or  stars  are,  in  consequence 


28  NOTES  ON  LIGHT. 

of  the  immense  distances  of  these  objects,  sensibly  par- 
allel. 

81.  By  suitably  reflecting  them,  we  can  render  the 
rays  from  terrestrial  sources  either  parallel  or  convergent. 
This  is  done  by  means  of  concave  mirrors. 

82.  In  its  reflection  from  such  mirrors,  light  obeys  the 
law  already  enunciated  for  plane  mirrors.     The  angle  of 
incidence  is  equal  to  the  angle  of  reflection. 

FIG.  1. 

M 


83.  Let  M  N  be  a  very  small  portion  of  the  circum- 
ference of  a  circle  with  its  centre  at  O.     Let  the  line  a  or, 
passing  through  the  centre,  cut  the  arc  M  N"  into  two  equal 
parts  at  a.     Then  imagine  the  curve  M  N  twirled  round 
a  x  as  a  fixed  axis ;  the  curve  would  describe  part  of  a 
spherical  surface.     Suppose  the  surface  turned  toward  x  to 
be  silvered  over,  we  should  then  have  a  concave  spherical 
reflector ;  and  we  have  now  to  understand  the  action  of 
this  reflector  upon  light. 

84.  The  line  a  x  is  the  principal  axis  of  the  mirror. 
.85.  All  rays  from  a  point  placed  at  the  centre  O  strike 

the  surface  of  the  mirror  as  perpendiculars,  and  after  re- 
flection return  to  O. 

86.  A  luminous  point  placed  on  the  axis  beyond  O,  say 


REFLECTION   FROM   CURVED   SURFACES.  29 

at  jc,  throws  a  divergent  cone  of  rays  upon  the  mirror. 
These  rays  are  rendered  convergent  on  reflection,  and  they 
intersect  each  other  at  some  point  on  the  axis  between  the 
centre  O  and  the  mirror.  In  every  case  the  direct  and  the 
reflected  rays  (xm  and  mx'  for  example)  enclose  equal 
angles  with  the  radius  (O  m)  drawn  to  the  point  of  inci- 
dence. 

87.  Supposing  x  to  be  exceedingly  distant,  say  as  far 
away  as  the  sun  from  the    small  mirror — or,  more  cor- 
rectly, supposing  it  to  be  infinitely  distant— then  the  rays 
falling  upon  the  mirror  will  be  parallel.     After  reflection 
such  rays  intersect  each  other,  at  a  point  midway  between 
the  mirror  and  its  centre. 

88.  This  point,  which  is  marked  F  in  the  figure,  is  the 
principal  focus  of  the  mirror  ;  that  is  to  say,  the  principal 
focus  is  the  focus  of  parallel  rays. 

89.  The  distance  between  the  surface  of  the  mirror  and 
its  principal  focus  is  called  the  focal  distance. 

90.  In  optics,  the  position  of  an  object  and  of  its  image 
are  always  exchangeable.     If  a  luminous  point  be  placed 
in  the  principal  focus,  the  rays  from  it  will,  after  reflection, 
be  parallel.     If  the  point  be  placed  anywhere  between  the 
principal  focus  and  the  centre  O,  the  rays  after  reflection 
will  cut  the  axis  at  some  point  beyond  the  centre. 

91.  If  the  point  be  placed  between  the  principal  focus 
F  and  the  mirror,  the  rays  after  reflection  will  be  divergent 
— they  will  not  intersect  at  all — there  will  be  no  real  focus. 

92.  But  if  these  divergent  rays  be  produced  backward, 
they  will  intersect  behind  the  mirror,  and  form  there  what 
is  called  a  virtual,  or  imaginary  focus. 

Before  proceeding  further,  it  is  necessary  that  these 
simple  details  should  be  thoroughly  mastered.  Given  the 
position  of  a  point  in  the  axis  of  a  concave  mirror,  no  dif- 


30  NOTES  ON  LIGHT. 

ficulty  must  be  experienced  in  finding  the  position  of  the 
image  of  that  point,  nor  in  determining  whether  the  focus 
is  virtual  or  real. 

93.  It  will  thus  become  evident  that,  while  a  point 
moves  from  an  infinite  distance  to  the  centre  of  a  spherical 
mirror,  the  image  of  that  point  moves  only  over  the  dis- 
tance between  the  principal  focus  and  the  centre.     Con- 
versely, it  will  be  seen  that  during  the  passage  of  a  lumi- 
nous point  from  the  centre  to  the  principal  focus,  the 
image  of  the  point  moves  from  the  centre  to  an  infinite 
distance. 

94.  The  point  and  its  image  occupy  what  are  called 
conjugate  foci.     If  the  last  note  be  understood,  it  will  be 
seen  that  the  conjugate  foci  move  in  opposite  directions, 
and  that  they  coincide  at  the  centre  of  the  mirror. 

95.  If  instead  of  a  point  an  object  of  sensible  dimen- 
sions be  placed  beyond  the  centre  of  the  mirror,  an  in- 
verted image  of  the   object  diminished  in  size  will  be 
formed  between  the  centre  and  the  principal  focus. 

96.  If  the  object  be  placed  between  the  centre  and  the 
principal  focus,  an  inverted  and  magnified  image  of  the 
object  will  be  formed  beyond  the  centre.     The  positions 
of  the  image  and  its  object  are,  it  will  be  remembered, 
convertible. 

97.  In  the  two  cases  mentioned  in  95  and  96  the  image 
is  formed  in  the  air  in  front  of  the  mirror.     It  is  a  real 
image.     But  if  the  object  be  placed  between  the  principal 
focus  and  the  mirror,  an  erect  and  magnified  image  of  the 
object  is  seen  behind  the  mirror.  The  image  is  here  virtual. 
The  rays  enter  the  eye  as  if  they  came  from  an  object  be- 
hind the  mirror. 

98.  It  is  plain  that  the  images  seen  in  a  common  look- 
ing-glass are  all  virtual  images. 

99.  It  is  now  to  be  noted  that  what  has  been  here 


CAUSTICS  BY  REFLECTION.  31 

stated  regarding  the  gathering  of  rays  to  a  single  focus 
by  a  spherical  mirror  is  only  true  when  the  mirror  forms 
a  small  fraction  of  the  spherical  surface.  Even  then  it  is 
only  practically,  not  strictly  and  theoretically,  true. 

Caustics  by  Reflection  (  Catacaustics). 

100.  When  a  large  fraction  of  the  spherical  surface  is 
employed  as  a  mirror,  the  rays  are  not  all  collected  to  a 
point;  their  intersections,  on  the  contrary,  form  a  lumi- 
nous surface,  which  in  optics  is  called  a  caustic  (German, 
Brennflache). 

101.  The  interior  surface  of  a  common  drinking-glass 
is  a  curved  reflector.     Let  the  glass  be  nearly  filled  with 
milk,  and  a  lighted  candle  placed  beside  it;  a  caustic 
curve  will  be  drawn  upon  the  surface  of  the  milk.     A 
carefully-bent  hoop,  silvered  within,  also  shows  the  caustic 
very  beautifully.     The  focus  of  a  spherical  mirror  is  the 
cusp  of  its  caustic. 

102.  Aberration. — The  deviation  of  any  ray  from  this 
cusp  is  called  the  aberration  of  the  ray.     The  inability  of 
a  spherical  mirror  to  collect  all  the  rays  falling  upon  it 
to  a  single  point  is  called  the  spherical  aberration  of  the 
mirror. 

103.  Heal  images,  as  already  stated,  are  formed  in  the 
air  in  front  of  a  concave  mirror,  and  they  may  be  seen 
in  the  air  by  an  eye  placed  among  the  divergent  rays  be- 
yond the  image.     If  an  opaque  screen,  say  of  thick  paper, 
intersect  the  image,  it  is  projected  on  the  screen  and  is 
seen  in  all  positions  by  an  eye  placed  in  front  of  the  screen. 
If  the  screen  be  semi-transparent,  say  of  ground  glass  or 
tracing-paper,  the  image  is  seen  by  an  eye  placed  either  in 
front  of  the  screen  or  behind  it.     The  images  in  phantas- 
magoria are  thus  formed. 

Concave  spherical  surfaces  are  usually  employed  as 


32  NOTES  ON   LIGHT. 

burning-mirrors.  By  condensing  the  sunbeams  with  a 
mirror  3  feet  in  diameter  and  of  2  feet  focal  distance,  very 
powerful  effects  may  be  obtained.  At  the  focus,  water  is 
rapidly  boiled,  and  combustible  bodies  are  immediately 
set  on  fire.  Thick  paper  bursts  into  flame  with  explosive 
violence,  and  a  plank  is  pierced  as  with  a  hot  iron. 

Convex  Mirrors. 

104.  In  the  case  of  a  convex  spherical  mirror  the  posi- 
tions of  its  foci  and  of  its  images  are  found  as  in  the  case 
of  a  concave  mirror.     But  all  the  foci  and  all  the  images 
of  a  convex  mirror  are  virtual. 

105.  Thus  to  find  the  principal  focus  you  draw  parallel 
rays  which,  on  reflection,  enclose  angles  with  the  radii 
equal  to  those  enclosed  by  the  direct  rays.     The  reflected 
rays  are  here  divergent  /  but  on  being  produced  back- 
ward, they  intersect  at  the  principal  focus   behind  the 
mirror. 

106.  The  drawing  of  two  lines  suffices  to  fix  the  posi- 
tion of  the  image  of  any  point  of  an  object  either  in  con- 
cave or  convex  spherical  mirrors.     A  ray  drawn  from  the 
point  through  the  centre  of  the  mirror  will  be  reflected 
through  the  centre ;  a  ray  drawn  parallel  to  the  axis  of 
the  mirror  will,  after  reflection,  pass,  or  its  production 
will  pass,  through  the  principal  focus.     The  intersection 
of  these  two  reflected  rays  determines  the  position  of  the 
image  of  the  point.     Applying  this  construction  to  objects 
of  sensible  magnitude,  it  follows  that  the  image  of  an 
object  in  a  convex  mirror  is  always  erect  and  diminished. 

107.  If  the  mirror  be  parabolic  instead  of  spherical,  all 
parallel  rays  falling  upon  the  mirror  are  collected  to  a 
point  at  its  focus ;  conversely,  a  luminous  point  placed  at 
the  focus  sends  forth  parallel  rays :  there  is  no  aberration. 
If  the  mirror  be  elliptical,  all  rays  emitted  from  one  of  the 


REFRACTION   OF  LIGHT.  33 

foci  of  the  ellipsoid  are  collected  together  at  the  other. 
Parabolic  reflectors  are  employed  in  light-houses,  where 
it  is  an  object  to  send  a  powerful  beam,  consisting  of  rays 
as  nearly  as  possible  parallel,  far  out  to  sea.  In  this  case 
the  centre  of  the  flame  is  placed  in  the  focus  of  the  mirror ; 
but,  inasmuch  as  the  flame  is  of  sensible  magnitude,  and 
not  a  mere  point,  the  rays  of  the  reflected  beam  are  not 
accurately  parallel. 

The  Refraction  of  Light  (Dioptrics). 

108.  We  have  hitherto  confined  our  attention  to  the 
portion  of  a  beam  of  light  which  rebounds  from  the  re- 
flecting surface.     But,  in  general,  a  portion  of  the  beam 
also  enters  the  reflecting  substance,  being  rapidly  quenched 
when  the  substance  is  opaque  (see  note  11),  and  freely 
transmitted  when  the  substance  is  transparent. 

109.  Thus  in  the  case  of  water,  mentioned  in  note  60, 
when  the  incidence  is  perpendicular  all  the  rays  are  trans- 
mitted, save  the  18  referred  to  as  being  reflected.     That 
is  to  say,  982  out  of  every  1,000  rays  enter  the  water  and 
pass  through  it. 

110.  So  likewise  in  the  case  of  mercury,  mentioned  in 
the  same  note;  334  out  of  every  1,000  rays  falling  on  the 
mercury  at  a  perpendicular  incidence,  enter  the  metal  and 
are  quenched  at  a  minute  depth  beneath  its  surface. 

We  have  now  to  consider  that  portion  of  the  luminous 
beam  which  enters  the  reflecting  substance ;  taking,  as  an 
illustrative  case,  the  passage  from  air  into  water. 

111.  If  the  beam  fall  upon  the  water  as  a  perpendicu- 
lar, it  pursues  a  straight  course  through  the  water :  if  the 
incidence  be  oblique,  the  direction  of  the  beam  is  changed 
at  the  point  where  it  enters  the  water. 


34 


NOTES  ON  LIGHT. 


112.  This  bending  of  the  beam  is  called  refraction. 
Its  amount  is  different  in  different  substances. 


FIG.  2. 


m 


113.  The  refraction  of  light  obeys  a  perfectly  rigid 
law  which  must  be  clearly  understood.    Let  A  B  C  D,  Fig. 
2,  be  the  section  of  a  cylindrical  vessel  which  is  half  filled 
with  water,  its  surface  being  AC.     E  is  the  centre  of  the 
circular  section  of  the  cylinder,  and  B  D  is  a  perpendicular 
to  the  surface  at  E.     Let  the  cylindrical  envelope  of  the 
vessel  be  opaque,  say  of  brass  or  tin,  and  let  an  aperture 
be  imagined  in  it  at  B,  through  which  a  narrow  light- 
beam  passes  to  the  point  E.     The  beam  will  pursue  a 
straight  course  to  D  without  turning  to  the  right  or  to  the 
left. 

114.  Let  the  aperture  be  imagined  at  m,  the  beam 
striking  the  surface  of  the  water  at  E  obliquely.    Its  course 
on  entering  the  liquid  will  be  changed ;  it  will  pursue  the 
track  E  n. 

115.  Draw  the  line  m  o  perpendicular  to  B  D,  and  also 
the  line  n  p  perpendicular  to  the  same  B  D.     It  is  always 
found  that  m  o  divided  by  n  p  is  a  constant  quantity,  no 
matter  what  may  be  the  angle  at  which  the  ray  enters  the 
water. 


REFRACTION    OF  LIGHT.  35 

116.  The  angle  marked  x  above  the  surface  is  called 
the  angle  of  incidence ;  the  angle  at  y  below  the  surface 
is  called  the  angle  of  refraction ;  and  if  we  regard  the 
radius  of  the  circle  A  B  C  D  as  unity  or  1,  the  line  m  o 
will  be  the  sine  of  the  angle  of  incidence ;  while  the  line 
n  p  will  be  the  sine  of  the  angle  of  refraction. 

11V.  Hence  the  ill-important  optical  law — The  sine  of 
the  angle  of  incidence  divided  by  the  sine  of  the  angle  of 
refraction  is  a  constant  quantity.  However  these  angles 
may  vary  in  size,  this  bond  of  relationship  is  never  severed. 
If  one  of  them  be  lessened  or  augmented,  the  other  must 
diminish  or  increase  so  as  to  obey  this  law.  Thus  if  the 
incidence  be  along  the  dotted  line  m'  E,  the  refraction  will 
be  along  the  line  E  n\  but  the  ratio  of  m'  o'  to  n'  p'  will 
be  precisely  the  same  as  that  of  m  o  to  n  p. 

118.  The  constant  quantity  here  referred  to  is  called 
the  index  of  refraction. 

119.  One  word  more  is  necessary  to  the  full  compre- 
hension of  the  term  sine,  and  of  the  experimental  demon- 
stration of  the  law  of  refraction.     When  one  number  is 
divided  by  another  the  quotient  is  called  the  ratio  of  the 
one  number  to  the  other.     Thus  1  divided  by  2  is  ^,  and 
this  is  the  ratio  of  1  to  2.    Thus  also  2  divided  by  1  is  2,  and 
this  is  the  ratio  of  2  to  1.     In  like  manner  12  divided  by 
3  is  4,  and  this  is  the  ratio  of  12  to  3.     Conversely,  3  di- 
vided by  12  is  ^,  and  this  is  the  ratio  of  3  to  12. 

120.  In  a  right-angled  triangle  the  ratio  of  any  side 
to  the  hypothenuse  is  found  by  dividing  that  side  by  the 
hypothenuse.     This  ratio  is  the  sine  of  the  angle  opposite 
to  the  side,  however  large  or  small  the  triangle  may  be. 
Thus  in  Fig.  2  the  sine  of  the  angle  x  in  the  right-angled 
triangle  E  o  m  is  really  the  ratio  of  the  line  o  m  to  the 
hypothenuse  E  m  •  it  would  be  expressed  in  a  fractional 

form  thus,  ^ — .     In  like  manner  the  sine  of  y  is  the  ratio 
Hi  m 


36  NOTES  ON  LIGHT, 

of  the  line  np  to  the  hypothenuse  E  w,  and  would  be  ex- 
pressed in  a  fractional  form  thus,  *j~.  These  fractions  are 

the  sines  of  the  respective  angles,  whatever  be  the  length 
of  the  line  E  m  or  E  n.  In  the  particular  case  above  re- 
ferred to,  where  these  lines  are  considered  as  units,  the 

f      , .       mo       _ n  p 

tractions  -y-  and  —--,  or  in  other  words  m  o  and  n  p^  be- 
come, as  stated,  the  sines  of  the  respective  angles.  We 
are  now  prepared  to  understand  a  simple  but  rigid  dem- 
onstration of  the  law  of  refraction. 

FIG.  3. 


r  H  -      - 

121.  ML  J  K  is  a  cell  with  parallel  glass  sides  and  one 
opaque  end  M  L»     The  light  of  a  candle  placed  at  A  falls 
into  the  vessel,  the   end  ML  casting  a  shadow  which 
reaches  to  the  point  E.     Fill  the  vessel  with  water — the 
shadow  retreats  to  PI  through  the  refraction  of  the  light 
at  the  point  where  it  enters  the  water. 

122.  The  angle  enclosed  between  M  E  and  M  L  is  equal 
to  the  angle  of  incidence  a?,  and,  in  accordance  with  the 

L 


definition  given  in  120,-^- ^   is  its  sine 

sine  of  the  angle  of  refraction  y.     All  these  lines  can  be 


while  -— -  is  the 


REFRACTION   OF   LIGHT.  37 

either  measured  or  calculated.  If  they  be  thus  determined, 
and  if  the  division  be  actually  made,  it  will  always  be  found 

T     TM  T      TT 

that  the  two  quotient  s-^-^  and  ^  ==rStand  in   a   constant 


ratio  to  each  other,  whatever  the  angle  may  be  at  which 
the  light  from  A  strikes  the  surface  of  the  liquid.     This 

4 
ratio  in  the  case  of  water  is  —  ,  or,  expressed  in  decimals, 

1.333.* 

123.  When  the  light  passes  from  air  into  water,  the 
refracted  ray  is  bent  toward  the  perpendicular.     This  is 
generally,  but  not  always,  the  case  when  the  light  passes 
from  a  rarer  to  a  denser  medium. 

124.  The  principle  of  reversibility  which  runs  through 
the  whole  of  optics  finds  illustration  here.     When  the  ray 
passes  from  water  to  air  it  is  bent/rom  the  perpendicular: 
it  accurately  reverses  its  course. 

125.  If  instead  of  water  we  employed  vinegar  the  ratio 
would  be  1.344  ;  with  brandy  it  would  be  1.360  ;  with  rec- 
tified spirit.  of  wine  1.372  ;  with  oil  of  almonds  or  with 
olive  oil  1.470;  with  spirit  of  turpentine  1.605;  wTithoilof 
aniseseed  1.538;  with  oil  of  bitter  almonds  1.471;  with 
bisulphide  of  carbon  1.678  ;  with  phosphorus  2.24. 

126.  These  numbers  express  the  indices  of  refraction 
of  the  various  substances  mentioned  ;  all  of  them  refract 
the  light  more  powerfully  than  water,  and  it  is  worthy  of 
remark  that,  all  of  them,  except  vinegar,  are  combustible 
substances. 

127.  It  was  the  observation  on  the  part  of  Newton, 
that,   having    regard    to   their  density,  "unctuous   sub- 
stances"  as   a  general  rule  refracted  light   powerfully, 
coupled  with  the  fact  that  the  index  of  refraction  of  the 
diamond  reached,  according.  to  his  measurements,  so  high 

.  *  More  accurately,  1.33G. 


38  NOTES   ON   LIGHT. 

a  figure  as  2.439,  that  caused  him  to  foresee  the  possible 
combustible  nature  of  the  diamond.  The  bold  prophecy 
of  Newton*  has  been  fulfilled,  the  combustion  of  a  dia- 
mond being  one  of  the  commonest  experiments  of  modern 
chemistry. 

128.  It  is  here  worth  noting  that  the  refraction  by 
spirit  of  turpentine  is  greater  than  that  by  water,  though 
the  density  of  the  spirit  is  to  that  of  the  water  as  874  is  to 
1,000.     A  ray  passing  obliquely  from  the  spirit  of  turpen- 
tine into  water  is  bent  from  the  perpendicular,  though  it 
passes  from  a  rarer  to  a  denser  medium ;  while  a  ray  pass- 
ing from  water  into  the  spirit  of  turpentine  is  bent  toward 
the  perpendicular,  though  it  passes  from  a  denser  to  a 
rarer  medium.     Hence  the  necessity  for  the  words  "  not 
always  "  employed  in  123. 

129.  If  a  ray  of  light  pass  through  a  refracting  plate 
with  parallel  surfaces,  or  through  any  number  of  plates 
with   parallel  surfaces,   on   regaining   the   medium  from 
which  it  started,  its  original  direction  is  restored.     This 
follows  from    the    principle    of   reversibility  already  re- 
ferred to. 

130.  In  passing  through  a  refracting  body,  or  through 
any  number  of  refracting  bodies,  the  light  accomplishes  its 
transit  in  the  minimum  of  time.     That  is  to  say,  given  the 
velocity  of  light  in  the  various  media,  the  path  chosen  by 
the  ray,  or,  in  other  words,  the  path  which  its  refraction 
imposes  upon  the  ray,  enables  it  to  perform  its  journey  in 
the  most  rapid  manner  possible. 

131.  Refraction  always  causes  water  to  appear  shal- 
lower, or  a  transparent  plate  of  any  kind  thinner,  than  it 

*  "  Car  ce  grand  homme,  qui  mettait  la  plus  grande  severitS  dans  ses 
experiences,  et  la  plus  grande  reserve  dans  ses  conjectures,  n'hesitait 
jamais  a  suivre  les  consequences  d!une  verite  aussi  loin  qu'elle  pouvait 
le  conduire." — BIOT. 


OPACITY   OF   TRANSPARENT   MIXTURES.  39 

really  is.     The  lifting  up  of  the  lower  surface  of  a  glass 
cube,  through  this  cause,  is  very  remarkable. 

132.  To  understand  why  the  water  appears  shallower, 
fix  your  attention  on  a  point  at  its  bottom,  and  suppose 
the  line  of  vision  from  that  point  to  the  eye  to  be  perpen- 
dicular to  the  surface  of  the  water.     Of  all  rays  issuing 
from  the  point,  the  perpendicular  one  alone  reaches  the  eye 
without  refraction.     Those  close  to  the  perpendicular,  on 
emerging  from  the  water,  have  their  divergence  augmented 
by  refraction.    Producing  these  divergent  rays  backward, 
they  intersect  at  a  point  above  the  real  bottom,  and  at  this 
point  the  bottom  will  be  seen. 

133.  The  apparent  shallowness  is  augmented  by  looking 
obliquely  into  the  water. 

134.  In  consequence  of  this  apparent  rise  of  the  bottom, 
a  straight  stick  thrust  into  the  water  is  bent  at  the  surface 
from  the  perpendicular. 

Note  the  difference  between  the  deportment  of  the  stick 
and  of  a  luminous  beam.  The  beam  on  entering  the  water 
is  bent  toward  the  perpendicular. 

135.  This  apparent  lifting  of  the  bottom  when  water  is 
poured  into  a  basin  brings  into  sight  an  object  at  the  bot- 
tom of  the  basin  which  is  unseen  when  the  basin  is  empty. 

Opacity  of  Transparent  Mixtures. 

136.  Reflection  always  accompanies  refraction;  and  if 
one  of  these  disappear,  the  other  will  disappear  also.     A 
solid  body  immersed  in  a  liquid  having  the  same  refractive 
index  as  the  solid,  vanishes ;  it  is  no  more  seen  than  a  por- 
tion of  the  liquid  itself  of  the  same  size  would  be  seen. 

137.  But  in  the  passage  from  one  medium  to  another 
of  a  different  refractive  index,  light  is  always  reflected ; 
and  this  reflection  may  be  so  often  repeated  as  to  render 
the  mixture  of  two  transparent  substances  practically  im- 


40  NOTES  ON  LIGHT. 

pervious  to  light.  It  is  the  frequency  of  the  reflections  at 
the  limiting  surfaces  of  air  and  water  that  renders  foam 
opaque.  The  blackest  clouds  owe  their  gloom  to  this  re- 
peated reflection,  which  diminishes  their  transmitted  light. 
Hence  also  their  whiteness  by  reflected  light.  To  a  similar 
cause  is  due  the  whiteness  and  imperviousiiess  of  common 
salt,  and  of  transparent  bodies  generally  when  crushed  to 
powder.  The  individual  particles  transmit  light  freely; 
but  the  reflections  at  their  surfaces  are  so  numerous  that 
the  light  is  wasted  in  echoes  before  it  can  reach  to  any 
depth  in  the  powder. 

138.  The  whiteness  and  opacity  of  writing-paper  are 
due  mainly  to  the  same  cause.     It  is  a  web  of  transparent 
fibres,  not  in  optical  contact,  which  intercept  the  light  by 
repeatedly  reflecting  it. 

139.  But  if  the  interstices  of  the  fibres  be  filled  by  a 
body  of  the  same  refractive  index  as  the  fibres  themselves, 
the  reflection  at  their  limiting  surfaces  is  destroyed,  and 
the  paper  is  rendered  transparent.     This  is  the  philosophy 
of  the  tracing-paper  used  by  engineers.     It  is  saturated 
with  some  kind  of  oil,  the  lines  of  maps  and  drawings 
being  easily  copied  through  it  afterward.     Water  aug- 
ments the  transparency  of  paper,  as  it  darkens  a  white 
towel ;  but  its  refractive  index  is  too  low  to  confer  on 
either  any  high   degree   of  transparency.     It,  however, 
renders  certain  minerals,  which  are   opaque   when  dry, 
translucent. 

140.  The  higher  the  refractive  index  the  more  copious 
is  the  reflection.     The  refractive  index  of  water,  for  ex- 
ample, is  1.336;  that  of  glass  is  1.5.     Hence  the  different 
quantities  of  light  reflected  by  water  and  glass  at  a  per- 
pendicular incidence,  as  mentioned  in  note  60.     It  is  its 
enormous  refractive  strength  that  confers  such  brilliancy 
upon  the  diamond. 


TOTAL   REFLECTION.  41 


Total  Reflection. 

Read  notes  123  and  124  ;  then  continue  here. 

141.  When  the  angle  of  incidence  from  air  into  water 
is  nearly  90°,  that  is  to  say,  when  the  ray  before  entering 
the  water  just  grazes  its  surface,  the  angle  of  refraction  is 
"48^°.     Conversely,  when  a  ray  passing  from  water  into  air 
strikes  the  surface  at  an  angle  of  48J-0,  it  will,  on  its  emer- 
gence, just  graze  the  surface  of  the  water. 

142.  If  the  angle  which  the  ray  in  water  encloses  with 
the  perpendicular  to  the  surface  be  greater  than  48-|-°,  the 
ray  will  not  quit  the  water  at  all :  it  will  be  totally  reflected 
at  the  surface. 

143.  The  angle  which  marks  the  limit  where  total  re- 
flection begins  is  called  the  limiting  angle  of  the  medium. 
For  water  this  angle  is  48°  27',  for  flint  glass  it  is  38°  41', 
while  for  diamond  it  is  23°  42'. 

144.  Realize  clearly  that  a  bundle  of  light  rays  filling 
an  angular  space  of  90°  before  they  enter  the  water,  are 
squeezed  into  an  angular  space  of  48°  27'  within  the  water, 
and  that  in  the  case  of  diamond  the  condensation  is  from 
90°  to  23°  42'. 

145.  To  an  eye  in  still  water  its  margin  must  appear- 
lifted  up.     A  fish,  for  example,  sees  objects,  as  it  were, 
through  a  circular  aperture  of  about  97°  (twice  47°  27')  in 
diameter  overhead.     All  objects  down  to  the  horizon  will 
be  visible  in  this  space,  and  those  near  the  horizon  will  be 
much  distorted  and  contracted  in  dimensions,  especially  in 
height.     Beyond  the  limits  of  this  circle  will  be  seen  the 
bottom  of  the  water  totally  reflected,  and  therefore  de- 
picted as  vividly  as  if  seen  by  direct  vision.* 

146.  A  similar  effect,  exerted  by  the  atmosphere  (when 

16  Sir  John  Hcrschcl. 


42  NOTES  ON   LIGHT. 

no  clouds  cross  the  orbs),  gives  the  sun  and  moon  at  rising 
and  setting  a  slightly  flattened  appearance. 

147.  Experimental  Illustrations. — Place  a  shilling  in  a 
drinking-glass  ;  cover  it  with  water  to  about  the  depth  of 
an  inch,  and  tilt  the  glass  so  as  to  obtain  the  necessary 
obliquity  of  incidence   at   the   surface.     Looking  upward 
toward  the  surface,  the  image  of  the  shilling  will  be  seen 
shining  there,  and,  as  the  reflection  is  total,  the  image  will 
be    as  bright    as   the  shilling   itself.     A  spoon   suitably 
dipped  into  the  glass  also  yields  an  image  due  to  total  re- 
flection. 

148.  Thrust  the  closed  end  of  an  empty  test-tube  into 
a  glass  of  water.     Incline  the  tube,  until  the  horizontal 
light  falling  upon  it  shall  be  totally  reflected  upward. 
When  looked  down  upon,  the  tube  appears  shining  like 
burnished  silver.    Pour  a  little  water  into  the  tube  :  as  the 
liquid  rises,  it  abolishes  total  reflection,  and  with  it  the 
lustre,  leaving  a  gradually  diminishing  lustrous  zone,  which 
disappears  wholly  when  the  level  of  the  water  within  rises 
to,  or  above,  that  of  the  water  without.     A  tube  of  any 
kind  stopped  water-tight  will  answer  for  this  experiment, 
which  is  both  beautiful  and  instructive. 

149.  If  a  ray  of  light  fall  as  a  perpendicular  on  the 
side  of  a  right-angled  isosceles  glass  prism,  it  will  enter 
the  glass  and  strike  the  hypothenuse  at  an  angle  of  45°. 
This  exceeds  the  limiting  angle  of  glass ;   the  ray  will 
therefore  be  totally  reflected ;  and,  in  accordance  with  the 
law  mentioned  in  note  54,  the  direct  and  reflected  rays 
will  be  at  right  angles  to  each  other.     When  such  a  change 
of  direction  is  required  in  optical  instruments,  a  right- 
angled  isosceles  prism  is  usually  employed. 

150.  When  the  ray  enters  the  prism  parallel  to  the 
hypothenuse,  it  will  be  refracted,  and  will  strike  the  hy- 
pothenuse at  an  angle  greater  than  the  limiting  angle.     It 


TOTAL  REFLECTION.  43 

will,  therefore,  be  totally  reflected.  If  the  object,  instead 
of  being  a  point,  be  of  sensible  magnitude,  the  rays  from 
its  extremities  will  cross  each  other  within  the  prism,  and 
hence  the  object  will  appear  inverted  when  looked  at 
through  the  prism.  Dove  has  applied  the  "  reversion  prism  " 
to  render  erect  the  inverted  images  of  the  astronomical 
telescope. 

151.  The  mirage  of  the  desert  and  various  other  phan- 
tasmal appearances  in  the  atmosphere  are,  in  part,  due  to 
total  reflection.     When  the  sun  heats  an  expanse  of  sand, 
the  layer  of  air  in  contact  with  the  sand  becomes  lighter 
than  the  superincumbent  air.     The  rays  from  a  distant 
object,  a  tree  for  example,  striking  very  obliquely  upon 
the  upper  surface  of  this  layer,  may  be  totally  reflected, 
thus  showing  images  similar  to  those  produced  by  a  sur- 
face of  water.     The  thirsty  soldiers  of  the  French  army 
were  tantalized  by  such  appearances  in  Egypt. 

152.  Gases,  like  liquids  and  solids,  can  refract  and  re- 
flect light ;  but,  in  consequence  of  the  lowness  of  their 
refractive  indices,  both  reflection  and  refraction  are  feeble. 
Still,  atmospheric  refraction  has  to  be  taken  into  account 
by  the  astronomer,  and  by  those  engaged  in  trigonomet- 
rical surveys.     The  refraction  of  the  atmosphere  causes 
the  sun  to  be  seen  before  it  actually  rises,  and  after  it  act- 
ually sets. 

153.  The  quivering  of  objects  seen  through  air  rising 
over  a  heated  surface  is  due  to  irregular  refraction,  which 
incessantly  shifts   the    directions    of  the  rays  of  light. 
In   the  air  this  shifting   of  the   rays   is   never   entirely 
absent,  and  it  is  often  a  source  of  grievous  annoyance 
to  the   astronomer  who    needs   a   homogeneous    atmos- 
phere. 

154.  The  flame  of  a  candle  or  of  a  gas-lamp,  and  the 
column  of  heated  air  above  the  flame ;  the  air  rising  from 


44  NOTES  ON   LIGHT. 

a  red-hot  iron ;  the  pouring  of  a  heavy  gas,  such  as  car- 
bonic acid,  downward  into  air;  and  the  issue  of  a  lighter 
one,  such  as  hydrogen,  upward  —  may  all  be  made  to 
reveal  themselves  by  their  action  upon  a  sufficiently  in- 
tense light.  The  transparent  gases  interposed  between 
such  a  light  and  a  white  screen  are  seen  to  rise  like  smoke 
upon  the  screen  through  the  effects  of  refraction. 

Lenses. 

155.  A  lens  in  optics  is  a  portion  of  a  refracting  sub- 
stance, such  as  glass,  which  is  bounded  by  curved  sur- 
faces.    If  the  surface  be  spherical,  the  lens  is  called  a 
spherical  lens. 

156.  Lenses  divide  themselves  into  two  classes,  one  of 
which  renders  parallel  rays  convergent,  the  other  of  which 
renders  such  rays  divergent.     Each  class  comprises  three 
kinds  of  lenses,  which  are  named  as  follows : 

Converging  Lenses. 

1.  Double  convex,  with  both  surfaces  convex. 

2.  Plano-convex,  with  one  surface  plane  and  the  other 
convex. 

3.  Concavo-convex  (Meniscus),  with  a  concave  and 
a  convex   surface,  the   convex   surface   being  the   most 
strongly  curved. 

Diverging  Lenses. 

1.  Double  concave,  with  both  surfaces  concave. 

2.  Plano-concave,  with  one  surface  plane  and  the 
other  concave. 

3.  Convexo-concave,  with  a  convex  and  a  concave 
surface,  the   concave   surface   being  the  most   strongly 
curved. 


LENSES.  45 

157.  A  straight  line  drawn  through  the  centre  of  the 
lens,  and  perpendicular  to  its  two  convex  surfaces,  is  the 
principal  axis  of  the  lens. 

158.  A  luminous  beam  falling  on  a  convex  lens  parallel 
to  the  axis,  has  its  constituent  rays  brought  to  intersec- 
tion at  a  point  in  the  axis  behind  the  lens.     This  point  is 
the  principal  focus  of  the  lens.     As  before,  the  principal 
focus  is  the  focus  of  parallel  rays. 

159.  The  rays  from  a  luminous  point  placed  beyond 
the  focus  intersect  at  the  opposite  side  of  the  lens,  an 
image  of  the  point  being  formed  at  the  place  of  intersec- 
tion.    As  the  point  approaches  the   principal  focus  its 
image  retreats   from  it,   and  when  the   point    actually 
reaches  the  principal  focus,  its  image  is  at  an  infinite 
distance. 

160.  If  the  principal  focus  be  passed,  and  the  point 
come  between  that  focus  and  the  lens,  the  rays  after  pass- 
ing through  the  lens  will  be  still  divergent.     Producing 
them  backward,  they  will  intersect  on  that  side  of  the 
lens  on  which  stands  the  luminous  point.     The  focus  here 
is  virtual.     A  body  of  sensible  magnitude  placed  between 
the  focus  and  the  lens  would  have  a  virtual  image. 

161.  When  an  object  of  sensible  dimensions  is  placed 
anywhere  beyond  the  principal  focus,  a  real  image  of  the 
object  will  be  formed  in  the  air  behind  the  lens.     The 
image  maybe  either  greater  or  less  than  the  object  in  size, 
but  the  image  will  always  be  inverted. 

162.  The  .positions  of  the  image  and  the  object  are,  as 
before,  convertible. 

163.  In  the  case  of  concave  lenses  the  images  are  al- 
ways virtual. 

164.  A  spherical  lens  is  incompetent  to  bring  all  the 
rays  that  fall  upon  it  to  the  same  focus.     The  rays  which 
pass  through  the  lens   near  its  circumference  are  more 


46  NOTES  ON  LIGHT. 

refracted  than  those  which  pass  through  the  central  por- 
tions, and  they  intersect  earlier.  Where  perfect  definition 
is  required  it  is  therefore  usual,  though  at  the  expense  of 
illumination,  to  make  use  of  the  central  rays  only. 

165.  This  difference  of  focal  distance  between  the  cen- 
tral and  circumferential  rays  is  called  the  spherical  aberra- 
tion of  the  lens.     A  lens  so  curved  as  to  bring  all  rays  to 
the  same  focus  is  called  aplanatic  /  a  spherical  lens  cannot 
be  rendered  aplanatic. 

166.  As  in  the  case  of  spherical  mirrors,  spherical  lenses 
have  their  caustic  curves  and  surfaces  (diacaustics)  formed 
by  the  intersection  of  the  refracted  rays. 

"Vision  and  the  Eye. 

167.  The  human  eye  is  a  compound  lens,  consisting 
of  three  principal  parts :  the  aqueous  humor,  the  crystal- 
line lens,  and  the  vitreous  humor. 

1C  8.  The  aqueous  humor  is  held  in  front  of  the  eye  by 
the  cornea,  a  transparent,  horny  capsule,  resembling  a 
watch-glass  in  shape.  Behind  the  aqueous  humor,  and 
immediately  in  front  of  the  Crystalline  lens,  is  the  iris, 
which  surrounds  the  pupil.  Then  follow  the  lens  and 
the  vitreous  humor,  which  last  constitutes  the  main  body 
of  the  eye.  The  average  diameter  of  the  human  eye  is 
10.9  lines.* 

169.  When  the  optic  nerve  enters  the  eye  from  behind, 
.it  divides  into  a  series  of  filaments,  which  are  woven  to- 
gether to  form  the  retina,  a  delicate  net-work  spread  as  a 
screen  at  the  back  of  the  eye.  The  retina  rests  upon  a 
black  pigment,  which  reduces  to  a  minimum  all  internal 
reflection. 

1*70.  By  means  of  the  iris  the  size  of  the  pupil  may  be 
caused  to  vary  within  certain  limits.  When  the  light  is 

*  A  line  is  -^  th  of  an  inch. 


VISION  AND  THE  EYE.  47 

feeble  the  pupil  expands, 'when  it  is  intense  the  pupil  con- 
tracts ;  thus  the  quantity  of  light  admitted  into  the  eye 
is,  to  some  extent,  regulated.  The  pupil  also  diminishes 
when  the  eye  is  fixed  upon  a  near  object,  and  expands 
when  it  is  fixed  upon  a  distant  one. 

171.  The  pupil  appears  black;  partly  because  of  the ' 
internal  black  coating,  but  mainly  for  another  reason. 
Could  we  illuminate  the  retina,  and  see  at  the  same  time 
the  illuminated  spot,  the  pupil  would  appear  bright.     But 
the  principle  of  reversibility,  so  often  spoken  of,  comes 
into  play  here.     The  light  of  the  illuminated  spot  in  re- 
turning outward  retraces  its  steps,  and  finally  falls  upon 
the  source  of  illumination.     Hence,  to  receive  the  return- 
ing rays,  the  observer's  eye  ought  to  be  placed  between 
the  source  and  the  retina.     But  in  this  position  it  would 
cut  off  the  illumination.     If  the  light  be  thrown  into  the 
eye  by  a  mirror  pierced  with  a  small  orifice,  or  with  a 
small  portion  of  the  silvering  removed,  then  the  eye  of 
the  observer  placed  behind  the  mirror,  and  looking  through 
the  orifice,  may  see  the  illuminated  retina.     The  pupil 
under  these  circumstances  glows  like  a  live  coal.     This  is 
the  principle  of  the  Ophthalmoscope  (Augenspiegel,  Helin- 
holtz),  an  instrument  by  which  the  interior  of  the  eye 
may  be  scanned,  and  its  condition  in  health  or  disease 
noted. 

172.  In  the  case  of  albinos,  or  of  white  rabbits,  the 
black  pigment  is  absent,  and  the  pupil  is  seen  red  by  light 
which  passes  through  the  sclerotica,  or  white  of  the  eye. 
When  this  light  is  cut  off,  the  pupil  of  an  albino  appears 
black.     In  some  animals  the  black  pigment  is  displaced 
by  a  reflecting  membrane,  the  tapetum.     It  is  the  light 
reflected  from  the  tapetum  which  causes  a  cat's  eye  to 
shine  in  partial  darkness.     The  light  in  this  case  is  not 
internal,  for  when  the  darkness  is  total  the  cat's  eyes  do 
not  shine. 


48  NOTES  ON  LIGHT. 

173.  In  the  camera  obscura'of  the  photographer  the 
images  of  external  objects  formed  by  a  convex  lens  are 
received  upon  a  plate  of  ground  glass,  the  lens  being 
pushed  in  or  out  until  the  image  upon  the  glass  is  sharply 
defined. 

174.  The  eye  is  a  camera  obscura,  with  its  refracting 
lenses,  the  retina  playing  the  part  of  the  plate  of  ground 
glass   in  the   ordinary   camera.     For  perfectly   distinct 
vision  it  is  necessary  that  the  image  upon  the  retina  should 
be  perfectly  defined ;  in  other  words,  that  the  rays  from 
every  point  of  the  object  looked  at  should  be  converged 
to  a  point  upon  the  retina. 

175.  The  image  upon  the  retina  is  inverted. 

Adjustment  of  the  Eye :   Use  of  Spectacles. 

176.  If  the  letters  of  a  book  held  at  some  distance  from 
the  eye  be  looked  at  through  a  gauze  veil  placed  nearer 
the  eye,  it  will  be  found  that  when  the  letters  are  seen 
distinctly,  the  veil  is  seen  indistinctly ;  conversely,  if  the 
veil  be  seen  distinctly,  the  letters  will  be  seen  indistinct- 
ly.    This  demonstrates  that  the  images  of  objects  at  dif- 
ferent distances  from  the  eye  cannot  be  defined  at  the  same 
time  upon  the  retina. 

177.  Were  the  eye  a  rigid  mass,  like  a  glass  lens,  in- 
capable of  change  of  form,  distinct  vision  would  only  be 
possible  at  one  particular  distance.     We  know,  however, 
that  the  eye  possesses  a  power  of  adjustment  for  different 
distances.     This  adjustment  is  effected,  not  by  pushing 
the  front  of  the  eye  backward  or  forward,  but  by  chan- 
ging the  curvature  of  the  crystalline  lens. 

178.  The  image  of  a  candle  reflected  from  the  forward 
or  backward  surface  of  the  lens  is  seen  to  diminish  when 
the  eye  changes  from  distant  to  near  vision,  thus  proving 


ADJUSTMENT  OF  THE  EYE:  USE  OF  SPECTACLES.  49 

'       ..«• 

the  curvature  of  the  lens  to  be  greater  for  near  than  for 
distant  vision. 

179.  The  principal  refraction  endured  by  rays  of  light 
in  crossing  the  eye  occurs  at  the  surface  of  the  cornea, 
where  the  passage  is  from  air  to  a  much  denser  medium. 
The  refraction  at  the  cornea  alone  would  cause  the  rays 
to  intersect  at  a  point   nearly  half  an  inch  behind  the 
retina.     The  convergence  is  augmented  by  the  crystalline 
lens,  which  brings  the  point  of  intersection  forward  to  the 
retina  itself. 

180.  A  line  drawn  through  the  centre  of  the  cornea 
and  the  centre  of  the  whole  eye  to  the  retina  is  called  the 
axis  of  the  eye.     The  length  of  the  axis,  even  in  youth,  is 
sometimes  too  small ;  in  other  words,  the  retina  is  some- 
times too  near  the  cornea ;  so  that  the  refracting  part  of 
the  organ  is  unable  to  converge  the  rays  from  a  luminous 
point  so  as  to  bring  them  to  a  point  upon  the  retina.     In 
old  age  also  the  refracting  surfaces  of  the  eye  are  slightly 
flattened,  and  thus  rendered  incompetent  to  refract  the 
rays  sufficiently.     In  both  these  cases  the  image  would  be 
formed  behind  the  retina,  instead  of  upon  it,  and  hence  the 
vision  is  indistinct. 

181.  The  defect  is  remedied  by  holding  the  object  at  a 
distance  from  the  eye,  so  as  to  lessen  the  divergence  of  its 
rays,  or  by  placing  in  front  of  the  eye  a  convex  lens,  which 
helps  the  eye  to  produce  the  necessary  convergence.    This 
is  the  use  of  spectacles. 

182.  The  eye  is  also  sometimes  too  long  in  the  direc- 
tion of  the  axis,  or  the  curvature  of  the  refracting  surfaces 
may  be  too  great.     In  either  case  the  rays  entering  the 
pupil  are  converged  so  as  to  intersect  before  reaching  the 
retina.   This  defect  is  remedied  either  by  holding  the  object 
very  close  to  the  eye,  so  as  to  augment  the  divergence  of 
its  rays,  thus  throwing  back  the  point  of  intersection  ;  or 

3 


50  NOTES  ON  LIGHT. 

by  placing  in  front  of  the  eye  a  concave  lens,  which  pro- 
duces the  necessary  divergence. 

183.  The  eye  is  not   adjusted   at  the  same  time  for 
equally-distant  horizontal  and  vertical  objects.     The  dis- 
tance of  distinct  vision  is  greater  for  horizontal  lines  than 
for  vertical  ones.     Draw  with  ink  two  lines  at  right  angles 
to  each  other,  the  one  vertical,  the  other  horizontal :  see 
one  of  them  distinctly  black  and  sharp  ;  the  other  appears 
indistinct,  as  if  drawn  in  lighter  ink.     Adjust  the  eye  for 
this  latter  line,  the  former  will  then  appear  indistinct. 
This  difference  in  the  curvature  of  the  eye  in  two  direc- 
tions may  sometimes  become  so  great  as  to  render  the 
application  of  cylindrical  lenses  necessary  for  its  correc- 
tion. 

The  Punctum  Ccecum. 

184.  The  spot  where  the  optic  nerve  enters  the  eye,  and 
from  which  it  ramifies  to  form  the  net-work  of  the  retina, 
is  insensible  to  the  action  of  light.    An  object  whose  image 
falls  upon  that  spot  is  not  seen.     The  image  of  a  clock- 
face,  of  a  human  head,  of  the  moon,  may  be  caused  to  fall 
upon  this  "  blind  spot,"  and  when  this  is  the  case  the  object 
is  not  visible. 

185.  To  illustrate  this  point,  proceed  thus :  Lay  two 
white  wafers  on  black  paper,  or  two  black  ones  on  white 
paper,  with  an  interval  of  3  inches  between  them.     Bring 
the  right  eye  at  a  height  of  10  or  11  inches  exactly  over 
the  left-hand  wafer,  so  that  the  line  joining  the  two  eyes 
shall  be  parallel  to  the  line  joining  the  two  wafers.  Closing 
the  left  eye,  and  looking  steadily  with  the  right  at  the 
left-hand  wafer,  the  right-hand  one  ceases  to  be  visible. 
In  this  position  the  image  falls  upon  the  "  blind  spot "  of 
the  right  eye.     If  the  eye  be  turned  in  the  least  degree  to 
the  right  or  left,  or  if  the  distance  between  it  and  the  paper 


PERSISTENCE   OF  IMPRESSIONS.  51 

be  augmented  or  diminished,  the  wafer  is  immediately 
seen.  Preserving  these  proportions  as  to  size  and  distance, 
objects  of  far  greater  dimensions  than  the  wafer  may  have 
their  images  thrown  upon  the  blind  spot,  and  be  obliter- 
ated. 

Persistence  of  Impressions. 

186.  An  impression  of  light  once  made  upon  the  retina 
does  not  subside  instantaneously.     An  electric  spark  is 
sensibly  instantaneous ;  but  the  impression  it  makes  upon 
the  eye  remains  for  some  time  after  the  spark  has  passed 
away.     This  interval  of  persistence  varies  with  different 
persons,  and  amounts  to  a  sensible  fraction  of  a  second. 

187.  If,  therefore,  a  succession  of  sparks  follow  each 
other  at  intervals  less  than  the  time  which  the  impression 
endures,  the  separate  impressions  will  unite  to  form  a  con- 
tinuous light.     If  a  luminous  point  be  caused  to  describe 
a  circle  in  less  than  this  interval,  the  circle  will  appear  as 
a  continuous  closed  curve.     From  this    cause,  also,  the 
spokes  of  a  rapidly-rotating  wheel  blend  together  to  a 
shadowy  surface.     Wheatstone's  Photometer  is  based  on 
this  persistence.     It  also  explains  the  action  of  those  instru- 
ments in  which  a  series  of  objects  in  different  positions 
being  brought  in  rapid  succession  before  the  eye,  the  im- 
pression of  motion  is  produced. 

188.  A  jet  of  water  descending  from  an  orifice  in  the 
bottom  of  a  vessel  exhibits  two  distinct  parts  :  a  tranquil 
pellucid  portion  near  the  orifice,  and  a  turbid  or  untranquil 
portion  lower  down.     Both  parts  of  the  jet  appear  equally 
continuous.     But  when  the  jet  in  a  dark  room  is  illumi- 
nated by  an  electric  spark,  all  the  turbid  portion  reveals 
itself  as  a  string  of  separate  drops  standing  perfectly  still. 
It  is  their  quick  succession  that  produces  the  impression 
of  continuity.  ,  The  most  rapid  cannon-ball,  illuminated  by 


52  NOTES  ON  LIGHT. 

a  flash  of  lightning,  would  be  seen  for  the  fraction  of  a 
second  perfectly  motionless  in  the  air. 

189.  The  eye  is  by  no  means  a  perfect  optical  instru- 
ment. It  suffers  from  spherical  aberration;  a  scattered 
luminosity,  more  or  less  strong,  always  surrounding  the 
defined  images  of  luminous  objects  upon  the  retina.  By 
this  luminosity  the  image  of  the  object  is  sensibly  increased 
in  size ;  but  with  ordinary  illumination  the  scattered  light 
is  too  feeble  to  be  noticed.  When,  however,  bodies  are 
intensely  illuminated,  more  especially  when  the  bodies  are 
small,  so  that  a  slight  extension  of  their  images  upon  the 
retina  becomes  noticeable,  such  bodies  appear  larger  than 
they  really  are.  Thus,  a  platinum- wire  raised  to  whiteness 
by  a  voltaic  current  has  its  apparent  diameter  enormously 
increased.  Thus  also  the  crescent  moon  seems  to  belong 
to  a  larger  sphere  than  the  dimmer  mass  of  the  satellite 
which  it  partially  clasps.  Thus  also,  at  considerable  dis- 
tances, the  parallel  flashes  sent  from  a  number  of  separate 
lamps  and  reflectors  in  a  light-house  encroach  upon  each 
other,  and  blend  together  to  a  single  flash.  The  white- 
hot  particles  of  carbon  in  a  flame  <jfeecribe  lines  of  light, 
because  of  their  rapid  upward  motion.  These  lines  are 
widened  to  the  eye ;  and  thus  a  far  greater  apparent  so- 
lidity is  imparted  to  the  flame  than  in  reality  belongs  to  it. 
189a.  This  augmentation  of  the  true  size  of  the  optical 
image  is  called  Irradiation. 

Bodies  seen  within  the  Eye. 

190.  Almost  every  eye  contains  bodies  more  or  less 
opaque  distributed  through  its  humors.  The  so-called 
muscce  volitantes  are  of  this  character ;  so  are  the  black 
dots,  snake-like  lines,  beads,  and  rings,  which  are  strikingly 
visible  in  many  eyes.  Were  the  area  of  the  pupil  con- 
tracted to  a  point,  such  bodies  might  produce  considerable 


lUJCM 


v  s*v^i  A 


BODIES  SEEN   WITHIN   THE  EYE.  53 

annoyance ;  but  because  of  the  width  of  the  pupil  the 
shadows  which  these  small  bodies  would  otherwise  cast 
upon  the  retina  are  practically  obliterated,  except  when 
they  are  very  close  to  the  back  of  the  eye.*  It  is  only 
necessary  to  look  at  the  firmament  through  a  pinhole  to 
give  these  shadows  greater  definition  upon  the  retina. 

191.  The  veins  and  arteries  of  the  retina  itself  also  cast 
their  shadows  upon  its  posterior  surface ;  but  the  shaded 
spaces  soon  become  so  sensitive  to  light  as  to  compensate 
for  the  defect  of  light  falling  upon  them.     Hence  under 
ordinary  circumstances  the  shadows  are  not  seen.     But  if 
the  shadows  be  transported  to  a  less  sensitive  portion  of 
the  retina,  the  image  of  the  vessels  becomes  distinctly 
visible. 

192.  The  best  mode  of  obtaining  the  transference  of  the 
shadow  is  to  concentrate  in  a  dark  room,  by  means  of  a 
pocket  lens  of  short  focus,  a  small  image  of  the  sun  or  of 
the  electric  light  upon  the  white  of  the  eye.     Care  must  be 
taken  not  to  send  the  beam  through  the  pupil.     When  the 
small  lens  is  caused  to  move  to  and  fro,  the  shadows  are 
caused  to  travel  over  different  portions  of  the  retina,  and  a 
perfectly  defined  image  of  the  veins  and  arteries  is  seen 
projected  in  the  darkness  in  front  of  the  eye. 

193.  Looking  into  a  dark  space,  and  moving  a  candle 
at  the  same  time  to  and  fro  beside  the  eye,  so  that  the  rays 
enter  the  pupil  very  obliquely,  the  shadow  of  the  retinal 
vessels  is  also  obtained.     In  some  eyes  the  suddenness  and 
vigor  with  which  the  spectral  image  displays  itself  are 
extraordinary ;  others  find  it  difficult  to  obtain  the  effect. 

194.  Finally,  a  delicate  image  of  the  vessels  maybe 
obtained  by  looking  through  a  pinhole  at  the  bright  sky, 
and  moving  the  aperture  to  and  fro. 

*  See  Notes  18  and  19. 


54  NOTES  ON  LIGHT. 


The  Stereoscope. 

195.  Look  with  one  eye  at  the  edge  of  the  hand,  so  that 
the  finger  nearest  the  eye  shall  cover  all  the  others.   Then 
open  the  second  eye  ;  by  it  the  other  fingers  will  be  seen 
foreshortened.     The  images  of  the  hand  therefore  within 
the  two  eyes  are  different. 

196.  These  two  images  are  projected  on  the  two  retinoe ; 
if  by  any  means  we  could  combine  two  drawings,  executed 
on  a  flat  surface,  so  as  to  produce  within  the  two  eyes  two 
pictures  similar  to  the  two  images  of  the  solid  hand,  we 
should  obtain  the  impression  of  solidity.     This  is  done  by 
the  stereoscope. 

197.  The  first  form  of  this  instrument  was  invented  by 
Sir  Charles  Wheatstone.   He  took  drawings  of  solid  objects 
as  seen  by  the  two  eyes,  and  looked  at  the  images  of  these 
drawings  in  two  plane  mirrors.     Each  eye  looked  at  the 
image  which  belonged  to   it,  and  the  mirrors  were  so 
arranged  that  the  images  overlapped,  thus  appearing  to 
come  from  the  same  object.     By  this  combination  of  its 
two  plane  projections,  the  object  sketched  was  caused  to 
start  forth  as  a  solid. 

198.  In  looking  at  and  combining  two  such  drawings, 
the  eyes  receive  the  same  impression,  and  go  through  the 
same  process  as  when  they  look  at  the  real  object.     We 
see  only  one  point  of  an  object  distinctly  at  a  time.     If  the 
different  points  of  an  object  be  at  different  distances  from 
the  eyes,  to  see  the  near  points  distinctly  requires  a  greater 
convergence  of  the  axes  of  the  eyes  than  to  see  the  distant 
ones.     Now,  besides  the  identity  of  the  retinal  images  of 
the  stereoscopic  drawings  with  those  of  the  real  object,  the 
eyes,  in  order  to  cause  the  corresponding  pairs  of  points  of 
the  two  drawings  to  coalesce,  have  to  go  through  the  same 


THE  STEREOSCOPE.  55 

variations  of  convergence  that  are  necessary  to  see  dis- 
tinctly the  various  points  of  the  actual  object.  Hence  the 
impression  of  solidity  produced  by  the  combination  of  such 
drawings. 

199.  Measure  the  distance  between  two  pairs  of  points, 
which  when   combined  by  the  stereoscope  present  two 
single  points  at  different  distances  from  the  eye.     The  dis- 
tance between  the   one  pair  will  be   greater  than   that 
between  the  other  pair.     Different  degrees  of  convergence 
are  therefore  necessary  on  the  part  of  the  eye  to  combine 
the  two  pairs  of  points.     It  is  to  be  noted  that  the  coales- 
cence produced  in  the  stereoscope  at  any  particular  moment 
is  only  partial.     If  one  pair  of  corresponding  points  be 
seen  singly,  the  others  must  appear  double.     This  is  also 
the  case  when  an  actual  solid  is  looked  at  with  both  eyes ; 
of  those  points  of  it  which  are  at  different  distances  from 
the  eyes  one  only  is  seen  singly  at  a  time. 

200.  The  impression  of  solidity  may  be  produced  in  an 
exceedingly  striking  manner  without  any  stereoscope  at 
all.     Most  easily,  thus :   Take  two  drawings — projections, 
as  they  are  called — of  the  frustum  of  a  cone  ;  the  one  as  it 
is  seen  by  the  right  eye,  the  other  as  it  is  seen  by  the  left. 
Holding  them  at  some  distance  from  the  eyes,  let  the  left- 
hand  drawing  be  looked  at  by  the  right  eye,  and  the  right- 
hand  drawing  by  the  left.     The  lines  of  vision  of  the  two 
eyes  here  cross  each  other ;  and  it  is  easy,  after  a  few  trials 
with  a  pencil-point  placed  in  front  of  the  eyes,  to  make  two 
corresponding  points  of  the  drawings  coincide.     The  mo- 
ment they  coincide,  the  combined  drawings  start  forth  as 
a  single  solid,  suspended  in  the  air  at  the  place  of  intersec- 
tion of  the  lines  of  vision.     It  depends  upon  the  character 
of  the  drawings  whether  the  inside  of  the  frustum  is  seen, 
or  the  outside,  whether  its  base  or  its  top  seems  nearest  to 
the  eye.     For  this  experiment  the  drawings  are  best  made 


56  NOTES  ON   LIGHT. 

in  simple  outline,  and  they  may  be  immensely  larger  than 
ordinary  stereoscopic  drawings. 

Take  notice  that  here  also  the  different  pairs  of  the 
corresponding  points  are  at  different  distances  apart. 
Two  corresponding  points,  for  example,  of  the  top  of  the 
frustum  will  not  be  the  same  distance  asunder  as  two 
points  of  the  base. 

201.,  Wheatstone's  first  instrument  is  called  the  Re- 
flecting Stereoscope;  but  the  methods  of  causing  draw- 
ings to  coalesce  so  as  to  produce  stereoscope  effects  are 
almost  numberless.  The  instrument  most  used  by  the 
public  is  the  Lenticular  Stereoscope  of  Sir  David  Brews- 
ter.  In  it  the  two  projections  are  combined  by  means  of 
two  half  lenses  with  their  edges  turned  inward.  The  len- 
ticular stereoscope  also  magnifies.* 

202.  It  has  been  stated  in  note  198  that  for  the  dis- 
tinct vision  of  a  near  point  a  greater  convergence  of  the 
lines  of  vision  of  the  two  eyes  is  necessary  than  that  of  a 
distant  one,  By  an  instrument  in  which  two  rectangular 
prisms  are  employed,!  the  rays  from  two  points  may  be 
caused  to  cross  before  they  enter  the  eyes,  the  convergence 
being  thus  rendered  greater  for  the  distant  point  than 
for  the  near  one.  The  consequence  of  this  is,  that  the 
near  point  appears  distant,  and  the  distant  point  near. 
This  is  the  principle  of  Wheatstone's  pseudoscope.  By 
this  instrument  convex  surfaces  are  rendered  concave,  and 
concave  surfaces  convex.  The  inside  of  a  hat  or  teacup 
may  be  thus  converted  into  its  outside,  while  a  globe  may 
be  seen  as  a  concave  spherical  surface. 

*  Fuller  and  clearer  information  regarding  the  stereoscope  will  be 
found  in  the  Journal  of  the  PJiotographic  Society,  vol.  iii.  pp.  96,  116, 
and  167. 

See  Note  150. 


THEORY   OF  EMISSION.  57 

Nature  of  Light ;   Physical  Theory  of  Reflection  and 
Refraction. 

It  is  now  time  to  redeem  to  some  extent  the  promise 
of  our  first  note,  that  the  "something"  which  excites  the 
sensation  of  light  should  be  considered  more  closely  sub- 
sequently. 

203.  Every  sensation  corresponds  to  a  motion  excited 
in  our  nerves.     In  the  sense  of  touch,  the  nerves   are 
moved  by  the  contact  of  the  body  felt ;  in  the  sense  of 
smell,  they  are  stirred  by  the  infinitesimal  particles  of  the 
odorous  body ;  in  the  sense  of  hearing,  they  are  shaken 
by  the  vibrations  of  the  air. 

Theory  of  Emission. 

204.  Newton  supposed  light  to  consist  of  small  parti- 
cles shot  out  with  inconceivable  rapidity  by  luminous 
bodies,  and  fine  enough  to  pass  through  the  pores  of  trans- 
parent media.     Crossing  the  humors  of  the  eye,  and  strik- 
ing the  optic  nerve  behind  the  eye,  these  particles  were 
supposed  to  excite  vision. 

205.  This   is   the   Emission    Theory  or    Corpuscular 
Theory  of  Light. 

206.  Considering  the  enormous  velocity  of  light,  the 
particles,  if  they  exist,  must  be  inconceivably  small ;  for 
if  of  any  conceivable  weight,  they  would  infallibly  destroy 
so  delicate  an  organ  as  the  eye.     A  bit  of  ordinary  mat- 
ter, one  grain  in  weight,  and  moving  with  the  velocity  of 
light,  would  possess  the  momentum  of  a  cannon-ball  150 
Ibs.  weight,  moving  with  a  velocity  of  1,000  feet  a  second. 

207.  Millions  of  these  light  particles,  supposing  them 
to  exist,  concentrated  by  lenses  and  mirrors,  have  been 
shot  against  a  balance   suspended  by  a  single  spider's 
thread;  this  thread,  though  twisted  18,000  times,  showed 


58  NOTES   ON  LIGHT. 

no  tendency  to  untwist  itself;  it  was  therefore  devoid  of 
torsion.  But  no  motion  due  to  the  impact  of  the  particles 
was  even  in  this  case  observed.* 

208.  If  light  consists  of  minute  particles,  they  must  be 
shot  out  with  the  same  velocity  by  all  celestial  bodies. 
This  seems  exceedingly  unlikely,  when  the  different  gravi- 
tating forces  of  such  different  masses  are  taken  into  ac- 
count.    By  the  attractions  of  such  diverse  masses,  the 
particles  would  in  all  probability  be  pulled  back  with  dif- 
ferent degrees  of  force. 

209.  If,  for  example,  a  fixed  star  of  the  sun's  density 
possessed  250  times  the  sun's  diameter,  its  attraction,  sup- 
posing light  to  be  acted  on  like  ordinary  matter,  would 
be  sufficient  to  finally  stop  the  particles  of  light  issuing 
from  it.     Smaller  masses  would  exert  corresponding  de- 
grees of  retardation ;  and  hence  the  light  emitted  by  dif- 
ferent bodies  would  move  with  different  velocities.     That 
such  is  not  the  case — that  light  moves  with  the  same  ve- 
locity whatever  be  its  source — renders  it  probable  that  it 
does  not  consist  of  particles  thus  darted  forth. 

But  a  more  definite  and  formidable  objection  to  the 
Emission  Theory  may  be  stated  after  we  have  made  our- 
selves acquainted  with  the  account  it  rendered  of  the  phe- 
nomena of  reflection  and  refraction. 

210.  In   direct   reflection,  according  to  the   emission 
theory,  the  light  particles  are  first  of  all  stopped  in  their 
course  by  a  repellent  force  exerted  by  the  reflecting  body, 
and  then  driven  in  the  contrary  direction  by  the  same 
force. 

211.  This  repulsion  is,  however,  selective.     The  reflect- 
ing substance  singles  out  one  portion  of  the  group  of  par- 
ticles composing  a  luminous  beam  and  drives  them  back ; 

*  Bennett,  Phil  Trans.,  1792. 


THEORY  OF  UNDULATION.  59 

but  it  attracts  the  remaining  particles  of  the  group  and 
transmits  them. 

212.  When  a  light  particle   approaches  a  refractive 
surface  obliquely,  if  the  particle  be  an  attracted  one,  it  is 
drawn  toward  the  surface,  as  an  ordinary  projectile  is 
drawn  toward  the  earth.     Refraction  is  thus  accounted 
for.     Like  the  projectile,  too,  the  velocity  of  the  light  par- 
ticle is  augmented  during  its  deflection  ;  it  enters  the  re- 
fracting medium  with  this  increased  velocity,  and  once 
within  the  medium,  the  attractions  before  and  behind  the 
particle  neutralizing  each  other,  the  increased  velocity  is 
maintained. 

213.  Thus,  it  is  an   unavoidable  consequence  of  the 
theory  of  Newton,  that  the  bending  of  a  ray  of  light  toward 
the   perpendicular   is   accompanied  by  an  augmentation 
of  velocity — that  light  in  water  moves  more  rapidly  than 
in  air,  in  glass  more  rapidly  than  in  water,  in  diamond 
more  rapidly  than  in  glass.     In  short,  that  the  higher  the 
refractive  index,  the  greater  the  velocity  of  the  light. 

214.  A  decisive  test  of  the  emission  theory  was  thus 
suggested,  and  under  that  test  the  theory  has  broken 
down.     For  it  has  been  demonstrated,  by  the  most  rigid 
experiments,  that  the  velocity  of  light  diminishes  as  the 
index  of  refraction  increases.     The  theory,  however,  had 
yielded  to  the  assaults  made  upon  it  long  before  this  par- 
ticular experiment  was  made. 

Theory  of  Undulation. 

215.  The  Emission  Theory  was  first  opposed  by  the 
celebrated  astronomer  Huyghens,  and  the  no  less  cele- 
brated mathematician  Euler,  both  of  whom  held  that  light, 
like  sound,  was  a  product  of  wave-motion.    Laplace,  Malus, 
Biot,  and  Brewster,  supported  Newton,  and  the  emission 
theory  maintained  its  ground  until  it  was  finally  over- 


60  NOTES  ON  LIGHT. 

thrown  by  the  labors  of  Thomas  Young  *  and  Augustin 
Fresnel. 

216.  These  two  eminent  philosophers,  while  adducing 
whole  classes  of  facts  inexplicable  by  the  emission  theory, 
succeeded  in  establishing  the  most  complete  parallelism 
between  optical  phenomena  and  those  of  wave-motion. 
The  justification  of  a  theory  consists  in  its  exclusive  com- 
petence to  account  for  phenomena.     On  such  a  basis  the 

Wave  Theory ,  or  the  Undulatory  Theory  of  light,  now 
rests,  and  every  day's  experience  only  makes  its  founda- 
tions more  secure.  This  theory  must  for  the  future 
occupy  much  of  our  attention. 

217.  In  the  case  of  sound,  the  velocity  depends  upon 
the  relation  of  elasticity  to  density  in  the  body  which 
transmits  the  sound.    The  greater  the  elasticity  the  greater 
is  the  velocity,  and  the  less  the  density  the  greater  is  the 
velocity.     To  account  for  the  enormous  velocity  of  propa- 
gation in  the  case  of  light,  the  substance  which  transmits 
it  is  assumed  to  be  of  both  extreme  elasticity  and  of  ex- 

*  Dr.  Young  was  appointed  Professor  of  Natural  Philosophy  in  the 
Royal  Institution,  August  3,  1801.  From  a  marble  slab  in  the  village 
church  of  Farnborough,  near  Bromley,  Kent,  I  copied,  on  the  llth  of 
April,  the  following  inscription  : 

"  Near  this  place  are  deposited  the  remains  of  THOMAS  YOUNG,  M.  D., 
Fellow  and  Foreign  Secretary  of  the  Royal  Society,  Member  of  the  Na- 
tional Institute  of  France.  A  man  alike  eminent  in  almost  every  depart- 
ment of  human  learning,  whose  many  discoveries  enlarged  the  bounds  of 
Natural  Science,  and  who  first  penetrated  the  obscurity  which  had  veiled 
for  ages  the  Hieroglyphics  of  Egypt. 

"  Endeared  to  his  friends  by  his  domestic  virtues,  Honored  by  the 
world  for  his  unrivalled  acquirements,  He  died  in  the  hope  of  the  resur- 
rection of  the  just. 

"Born  at  Milverton,  in  Somersetshire,  June  13,  1773. 

"Died  in  Park  Square,  London,  May  29,  1820, 

"  In  the  56th  year  of  his  age." 


THEORY  OF  UNDULATION.  61 

trcme  tenuity.     This  substance  is  called  the  Luminiferous 
ether. 

218.  It  fills  space;  it  surrounds  the  atoms  of  bodies; 
it  extends,  without  solution  of  continuity,  through  the 
humors  of  the  eye.     The  molecules  of  luminous  bodies  are 
in  a  state  of  vibration.     The  vibrations  are  taken  up  by 
the  ether,  and  transmitted  through  it  in  waves.     These 
waves  impinging  on  the  retina  excite  the  sensation  of 
light. 

219.  In  the  case  of  sound,  the  air-particles  oscillate  to 
and  fro  in  the  direction  in  which  the  sound  is  transmitted ; 
in  the  case  of  light,  the  ether  particles  oscillate  to  and  fro 
across  the  direction  in  which  the  light  is  propagated.     In 
scientific  language  the  vibrations  of  sound  are  longitudi- 
nal, while  the  vibrations  of  light  are  transversal.     In  fact, 
the  mechanical  properties  of  the  ether  are  rather  those  of 
a  solid  than  of  an  air. 

220.  The  intensity  of  the  light  depends  on  the  distance 
to  which  the  ether  particles  move  to  and  fro.     This  dis- 
tance is  called  the  amplitude  of  the  vibration.     The  in- 
tensity of  light  is  proportional  to  the  square  of  the  ampli- 
tude ;  it  is  also  proportional  to  the  square  of  the  maximum 
velocity  of  the  vibrating  particle. 

221.  The  amplitude  of  the  vibrations  diminishes  simply 
as  the   distance  increases ;    consequently  the  intensity, 
which  is  expressed  by  the  square  of  the  amplitude,  must 
diminish  inversely  as  the  square  of  the  distance.     This, 
in  the  language  of  the  wave  theory,  is  the  law  of  inverse 
squares. 

222.  The  reflection  of  ether  waves  obeys  the  law  es- 
tablished in  the  case  of  light.     The  angle  of  incidence  is 
demonstrably  equal  to  the  angle  of  reflection. 

223.  To  account  for  refraction,  let  us  for  the  sake  of 
simplicity  take  a  portion  of  a  circular  wave  emitted  by  the 


62  NOTES  ON  LIGHT. 

sun  or  some  other  distant  body.  A  short  portion  of  such 
a  wave  would  be  straight.  Suppose  it  to  impinge  from 
air  upon  a  plate  of  glass,  the  wave  being  in  the  first  in- 
stance parallel  to  the  surface  of  the  glass.  Such  a  wave 
would  go  through  the  glass  without  change  of  direction. 

224.  But  as  the  velocity  in  glass  is  less  than  the  veloci- 
ty in  air,  the  wave  would  be  retarded  on  passing  into  the 
denser  medium. 

225.  But  suppose  the  wave,  before  impact,  to  be  ob- 
lique to  the  surface  of  the  glass ;  that  end  of  the  wave 
which  first  reaches  the  glass  will  be  first  retarded,  the 
other  portions  being  held  back  in  succession.     This  retar- 
dation of  one  end  of  the  wave  causes  it  to  swing  round ; 
so  that  when  the  wave  has  fully  entered  the  glass  its  course 
is  oblique  to  its  first  direction.     It  is  refracted. 

226.  If  the  glass  into  which  the  wave  enters  be  a  plate 
with   parallel   surfaces,  the  portion  of  the  wave  which 
reached  the  upper  surface  first,  and  was  first  retarded, 
will  also  reach  its  under  surface  first,  and  escape  earliest 
from  the   retarding  medium.     This   produces  a  second 
swinging  round  of  the  wave,  by  which  its  original  direc- 
tion is  restored.     In  this  simple  way  the  Wave  Theory 
accounts  for  Refraction. 

227.  The  convergence  or  divergence  of  beams  of  light 
by  lenses  is  immediately  deduced  from  the  fact  that  the 
different  points  of  the  ether  wave  reach  the  lens,  and  are 
retarded  by  the  lens  in  succession, 

228.  The  density  of  the  ether  is  greater  in  liquids  and 
solids  than  in  gases,  and  greater  in  gases  than  in  vacuo. 
A  compressing  force  seems  to  be  exerted  on  the  ether  by 
the  molecules  of  these  bodies.     Now  if  the  elasticity  of  the 
ether  increased  in  the  same  proportion  as  its  density,  the 
one  would  neutralize  the  other,  and  we  should  have  no 
retardation  of  the  velocity  of  light.     The  diminished  ve- 


THEORY  OF   UNDULATION.  G3 

locity  in  highly-refracting  bodies  is  accounted  for  by  as- 
suming that  in  such  bodies  the  elasticity  in  relation  to  the 
density  is  less  than  in  vacuo.  The  observed  phenomena 
immediately  flow  from  this  assumption. 

229.  The  case  is  precisely  similar  to  that  of  sound  in  a 
gas  or  vapor  which  does  not  obey  the  law  of  Mariotte. 
The  elasticity  of  such  a  gas  or  vapor,  when  compressed, 
increases  less  rapidly  than  the  density ;  hence  the  dimin- 
ished velocity  of  the  sound. 

230.  But  we  are  able  to  give  a  more  distinct  statement 
as  to  the  influence  which  a  refracting  body  has  upon  the 
velocity  of  light.    Regard  the  lines  o  m  and  np  in  Fig.  2, 
Note  113.     These  two  lines  represent  the  velocities  of  light 
in  the  two  media  there  considered;  or,  expressed  more 
generally,  the  sine  of  the  angle  of  incidence  represents  the 
velocity  of  light  in  the  first  medium,  while  the  sine  of  the 
angle  of  refraction  represents  the  velocity  in  the  second. 
The  index  of  refraction  then  is  nothing  else  than  the  ratio 
of  the  two  velocities.     Thus  in  the  case  of  water,  where  the 
index  of  refraction  is  -f ,  the  velocity  in  air  is  to  its  velocity 
in  water  as  4  is  to  3.     In  glass  also,  where  the  index  of 
refraction  is  f ,  the  velocity  in  air  is  to  the  velocity  in  glass 
as  3  is  to  2.     In  other  words  the  velocity  of  light  in  air 
is  H  times  its  velocity  in  water,  and  1 J  times  its  velocity 
in  glass.     The  velocity  of  light  in  air  is  about  2£  times  its 
velocity  in  diamond,  and  nearly  three  times  its  velocity  in 
chromate  of  lead,  the   most   powerfully  refracting  sub- 
stance hitherto  discovered.     Strictly  speaking,  the  index 
of  refraction  refers  to  the  passage  of  a  ray  of  light,  not 
from  air,  but  from  a  vacuum,*  into  the  refracting  body. 
Dividing  the  velocity  of  light  in  vacuo  by  its  velocity  in 
the  refracting  substance,  the  quotient  is  the  index  of  re- 
fraction of  that  substance. 

*  That  is  to  say,  a  vacuum  save  as  regards  the  ether  itself 


\ 


64  NOTES  ON   LIGHT. 

231.  In  the  wave  theory,  the  rays  of  light  are  per- 
pendiculars to  the  waves  of  ether.     Unlike  the  icave,  the 
ray  has  no  material  existence ;  it  is  merely  a  direction. 

Prisms. 

232.  It  has  been  stated,  in  Note  129,  that  in  the  case 
of  a  plate  of  glass  with  parallel  surfaces,  the  direction 
possessed  by  an  oblique  ray,  prior  to  its  meeting  the  glass, 
is  restored  when  it  quits  the  glass.     This  is  not  the  case 
if  the  two  surfaces  at  which  the  ray  enters  and  emerges 
be  not  parallel. 

233.  When  the  ray  passes  through  a  wedge-shaped 
transparent  substance,  in  a  direction  perpendicular  to  the 
edge  of  the  wedge,  it  is  permanently  refracted.     A  body 
of  this  shape  is  called  a  prism  in  optics,  and  the  angle  en- 
closed by  the  two  oblique  sides  of  the  wedge  is  called  the 
refracting  angle. 

234.  The  larger  the  refracting  angle  the  greater  is  the 
deflection  of  the  ray  from  its  original  direction.     But  with 
the  self-same  prism  the  amount  of  the  refraction  varies 
with  the  direction  pursued  by  the  ray  through  the  prism. 

235.  When  that  direction  is  such  that  the  portion  of 
the  ray  within  the  prism  makes  equal  angles  with  the  two 
sides  of  the  prism,  or,  what  is  the  same,  with  the  ray  be- 
fore it  reaches  the  prism  and  after  it  has  quitted  it,  then 
the  total  refraction  is  a  minimum.    This  is  capable  both  of 
mathematical  and  experimental  proof;  and  on  this  result 
is  based  a  method  of  determining  the  index  of  refraction. 

236.  The  final  direction  of  a  refracted  ray  being  un- 
altered by  its  passage  through  glass  plates  with  parallel 
surfaces,  we  may  employ  hollow  vessels  composed  of  such 
plates    and    filled  with    liquids,    thus    obtaining    liquid 
prisms. 


PRISMATIC  ANALYSIS  OF  LIGHT;    DISPERSION.        G5 

Prismatic  Analysis  of  Light  /  Dispersion. 

237.  Newton  first  unravelled  the  solar  light,  proving 
it  to  be  composed  of  an  infinite  number  of  rays  of  different 
degrees  of  refrangibility ;  when  such  light  is  sent  through 
a  prism,  its  constituent  rays  are' drawn  asunder.     This  act 
of  drawing  apart  is  called  dispersion. 

238.  The  waves  of  ether  generated  by  luminous  bodies 
are  not  all  of  the  same  length ;  some  are  longer  than 
others.    In  refracting  substances  the  short  waves  are  more 
retarded  than  the  longer  ones ;  hence  the  short  waves  are 
more  refracted  than  the  long  ones.     This  is  the  cause  of 
dispersion. 

239.  The  luminous  image  formed  when  a  beam  of  white 
light  is  thus  decomposed  by  a  prism  is  called  a  spectrum. 
If  the  light  employed  be  that  of  the  sun,  the  image  is 
called  the  solar  spectrum. 

240.  The  solar  spectrum  consists  of  a  series  of  vivid 
colors,  which,  when  reblended,  produce  the  original  white 
light.     Commencing  with  that  which  is  least  refracted, 
we  have  the  following  order  of  colors  in  the  solar  spec- 
trum :   Red,  Orange,  Yellow,  Green,  Blue,  Indigo,  Violet. 

241.  The  Color  of  Light  is  determined  solely  by  its 
Wave-length. — The   ether  waves   gradually   diminish  in 

length  from  the  red  to  the  violet.  The  length  of  a  wave 
of  red  light  is  about  Saj00th  of  an  inch ;  that  of  the  wave  of 
violet  light  is  about  g7^00th  of  an  inch.  The  waves  which 
produce  the  other  colors  of  the  spectrum  lie  between  these 
extremes. 

242.  The  velocity  of  light  being  192,000  miles  in  a 
second,  if  we  multiply  this  number  by  39,000  we  obtain 
the  number  of  waves  of  red  light  in  192,000  miles;  the 
product  is  474,439,680,000,000.     All  these  leaves  enter  the 
eye  in  a  second.     In  the  same  interval  699,000,000,000,000 


66  NOTES  ON  LIGHT. 

waves  of  violet  light  enter  the  eye.     At  this  prodigious 
rate  is  the  retina  hit  by  the  waves  of  light. 

243.  Color,  in  fact,  is  to  light  what  pitch  is  to  sound. 
The  pitch  of  a  note  depends  solely  on  the  number  of 
aerial  waves  which  strike  the  ear  in  a  second.     The  color 
of  light  depends  on  the  number  of  ethereal  waves  which 
strike  the  eye  in  a  second.     Thus  the  sensation  of  red  is 
produced  by  imparting  to  the  optic  nerve  four  hundred 
and   seventy-four   millions   of    millions   of  impulses   per 
second,  while  the  sensation  of  violet  is  produced  by  im- 
parting to  the  nerve  six  hundred  and  ninety-nine  millions 
of  millions   of  impulses   per   second.      In  the   Emission 
Theory  numbers  not  less  immense  occur,  "  nor  is  there 
any  mode  of  conceiving  the  subject  which  does  not  call 
upon  us  to  admit  the  exertion  of  mechanical  forces  which 
may  well  be  termed  infinite."  * 

Invisible  Rays  ;  Calorescence  and  Fluorescence. 

244.  The  spectrum  extends  in  both  directions  beyond 
its  visible  limits.     Beyond  the  visible  red  we  have  rays 
which  possess  a  high  heating  power,  though  incompetent 
to  excite  vision ;  beyond  the  violet  we  have  a  vast  body 
of  rays  which,  though  feeble  as  regards  heat,  and  power- 
less as  regards  light,  are  of  the  highest  importance  be- 
cause of  their  capacity  to  produce  chemical  action. 

245.  In  the  case  of  the  electric  light,  the  energy  of  the 
non-luminous  calorific  rays  emitted  by  the  carbon  points 
is  about  eight  times  that  of  all  the  other  rays  taken  to- 
gether.    The  dark  calorific  rays  of  the  sun  also  probably 
exceed  many  times  in  power  the  luminous  solar  rays.     It 
is  possible  to  sift  the  solar  or  the  electric  beam  so  as  to 
intercept  the  luminous  rays,  while  the  non-luminous  ravs 
are  allowed  free  transmission. 

*  Sir  John  Herschel. 


INVISIBLE  RAYS.  67 

246.  In  this  way  perfectly  dark  foci  may  be  obtained 
where  combustible  bodies  may  be  burned,  non-refractory 
metals  fused,  and  refractory  ones  raised  to  the  tempera- 
ture of  whiteness.     The  non-luminous  calorific  rays  may 
be  thus  transformed  into  luminous  ones,  which  yield  all 
the  colors  of  the  spectrum.     This  passage,  by  the  inter- 
vention of  a  refractory  body,  from  the  non-luminous  to  the 
luminous  state,  is  called  Calorescence. 

247.  So  also  as  regards  the  ultra-violet  rays;  when 
they  are  permitted  to  fall  upon  certain  substances — the 
disulphate  of  quinine  for  example — they  render  the  sub- 
stance luminous ;  invisible  rays  are  thereby  rendered  visi- 
ble.    The  change  here  receives  the  name  of  Fluorescence. 

248.  In  calorescence  the  atoms  of  the  refractory  body 
are  caused  to  vibrate  more  rapidly  than  the  waves  which 
fall  upon  them ;  the  periods  of  the  waves  are  quickened  by 
their  impact  on  the  atoms.     The  refrangibility  of  the  rays 
is,  in  fact,  exalted.     In  fluorescence,  on  the  contrary,  the 
impact  of  the  waves  throws  the  molecules  of  the  fluores- 
cent body  into  vibrations  of  slower  periods  than  those 
of  the  incident  waves  ;  the  refrangibility  of  the  rays  is 
in  fact  lowered.     Thus  by  exalting  the  refrangibility  of 
the  ultra-red,  and  by  lowering   the  refrangibility  of  the 
ultra-violet  rays,  both  classes  of  rays  are  rendered  capable 
of  exciting  vision. 

249.  Though  the  term  is  by  no  means  faultless,  those 
rays,  both  ultra-red  and  ultra-violet,  which  are  incom- 
petent to   excite  vision,  are   called  invisible  rays.     In 
strictness  we  cannot  speak  of  rays  being  either  visible  or 
invisible ;  it  is  not  the  rays  themselves  but  the  objects 
they  illuminate  that   become  visible.      "  Space,  though 
travers'ed  by  the  rays  from  all  suns  and  all  stars,  is  itself 
unseen.     Not  even  the  ether  which  fills  space,  and  whose 
motions  are  the  light  of  the  world,  is  itself  visible."* 

*  "  Proceedings  of  the  Royal  Institution,"  vol.  v.,  p.  456. 


68  NOTES  0$  LIGHT. 

Doctrine  of  Visual  Periods. 

250.  A  string  tuned  to  a  certain  note  resounds  when 
that  note  is  sounded.     If  you  sing  into  an  open  piano,  the 
string  whose  note  is  in  unison  with  your  voice  will  be 
thrown  into  sonorous  vibration.     If  there  be  discord  be- 
tween the  note  and  the  string,  there  is  no  resonance, 
however  powerful  the  note  may  be.     A  particular  church- 
pane   is   sometimes   broken  by  a   particular   organ-peal, 
through  the  coincidence  of  its  period  of  vibration  with 
that  of  the  organ. 

251.  In  this  way  it  is  conceivable  that  a  feeble  note, 
through  the  coincidence  of  its  periods  of  vibration  with 
those  of  a  sounding  body,  may  produce  effects  which  a 
powerful  note,  because  of  its  non-coincidence,  is  unable  to 
produce. 

252.  This,  which  is  a  known  phenomenon  of  sound, 
helps  us  to  a  conception  of  the  deportment  of  the  retina 
toward  light.     The  retina,  or  rather  the  brain  in  which 
its  fibres  end,  is,  as  it  were,  attuned  to  a  certain  range  of 
vibrations,  and  it  is  dead  to  all  vibrations  which  lie  with- 
out that  range,  however  powerful  they  may  be. 

253.  The  quantity  of  wave-motion  sent  to  the  eye  at 
night,  by  a  candle  a  mile  distant,  suffices  to  render  the 
candle  visible.     Employing  the  powerful  ultra-red  rays  of 
the  sun,  or  of  the  electric  light,  it  is  demonstrable  that 
ethereal  waves  possessing  many  millions  of  times  the  me- 
chanical energy   of  those  which   produce  the   candle's 
light,  may  be  caused  to  impinge  upon  the  retina  with- 
out  exciting  any  sensation  whatever.     The  periods  of 
succession  of  the  waves,  rather  than  their  strength,  are 
here  influential. 

254.  When  in  music  two  notes  are  separated  from  each 
other  by  an  octave,  the  higher  note  vibrates  witli  twice 


DOCTRINE   OF  COLORS.  69 

the  rapidity  of  the  lower.  In  Note  241  the  lengths  of  the 
wave  of  red  light  and  of  violet  light  are  set  down  as  -g-g^oir 
of  an  inch  and  -^^nr  of  an  inck  respectively ;  but  these 
numbers  refer  to  the  mean  red  and  the  mean  violet.  The 
waves  of  the  extreme  violet  are  about  half  the  length  of 
those  of  the  extreme  red,  and  they  strike  the  retina  with 
double  the  rapidity  of  the  red.  While,  therefore,  the  music- 
al scale,  or  the  range  of  the  ear,  is  known  to  embrace  nearly 
eleven  octaves,  the  optical  scale,  or  range  of  the  eye,  is 
comprised  within  a  single  octave. 

Doctrine  of  Colors. 

255.  Natural  bodies  possess  the  power  of  extinguish- 
ing, or,  as  it  is  called,  absorbing  the  light  that  enters  them. 
This  power  of  absorption  is  selective,  and  hence,  for  the  most 
part,  arise  the  phenomena  of  color. 

256.  When  the  light  which  enters  a  body  is  wholly 
absorbed  the  body  is  black ;  a  body  which  absorbs  all  the 
waves  equally,  but  not  totally,  is  gray ;  while  a  body  which 
absorbs  the  various  waves  unequally  is  colored.     Color  is 
due  to  the  extinction  of  certain  constituents  of  the  white 
light  within  the  body,  the  remaining  constituents  which 
return  to  the  eye  imparting  to  the  body  its  color. 

25*7.  It  is  to  be  borne  in  mind  that  bodies  of  all  colors, 
illuminated  by  white  light,  reflect  white  light  from  their 
exterior  surfaces.  It  is  the  light  which  has  plunged  to  a 
certain  depth  within  the  body,  which  has  been  sifted  there 
by  elective  absorption,  and  then  discharged  from  the  body 
by  interior  reflection  that,  in  general,  gives  the  body  its 
color. 

258.  A  pure  red  glass  interposed  in  the  path  of  a  beam 
decomposed  by  a  prism,  either  before  or  after  the  act  of 
decomposition,  cuts  off  all  the  colors  of  the  spectrum  except 
the  red.  A  glass  of  any  other  pure  color  similarly  inter- 


70  NOTES  ON  LIGHT. 

posed  would  cut  off  all  the  spectrum  except  that  particular 
portion  which  gives  the  glass  its  color.  It  is,  however, 
extremely  difficult,  if  not  impossible,  to  obtain  pure  pig- 
ments of  any  kind.  Thus  a  yellow  glass  not  only  allows 
the  yellow  light  of  the  spectrum  to  pass,  but  also  a  portion 
of  the  adjacent  green  and  orange  ;  while  a  blue  glass  not 
only  allows  the  blue  to  pass,  but  also  a  portion  of  the  ad- 
jacent green  and  indigo. 

259.  Hence,  if  a  beam  of  white  light  be  caused  to  pass 
through  a  yellow  glass  and  a  blue  glass  at  the  same  time, 
the  only  transmissible  color  common  to  both  is  green. 
This  explains  why  blue  and  yellow  powders,  when  mixed 
together,  produce  green.     The  white  light  plunges  into 
the  powder  to  a  certain  depth,  and  is  discharged  by  inter- 
nal reflection,  minus  its  yellow  and. its  blue.     The  green 
alone  remains. 

260.  The  effect  is  quite  different  when,  instead  of  mix- 
ing blue  and  yellow  pigments,  we  mix  blue  and  yellow 
lights  together.     Here  the  mixture  is  a  pure  white.     Blue 
and  yellow  are  complementary  colors. 

261.  Any  two  colors  whose  mixture  produces  white  are 
called  complementary  colors.     In  the  spectrum  we  have 
the  following  pairs  of  such  colors  : 

Red  and  greenish  Blue. 
Orange  and  cyanogen  Blue. 
Yellow  and  indigo  Blue. 
Greenish  Yellow  and  Violet. 

262.  A  body  placed  in  a  light  which  it  is  incompetent 
to  transmit  appears  black,  however  intense  may  be  the 
illumination.     Thus,  a  stick  of  red  sealing-wax,  placed  in 
the  vivid  green  of  the  spectrum,  is  perfectly  black.     A 
bright-red  solution  similarly  placed  cannot  be  distinguished 
from  black  ink ;  and  red  cloth,  on  which  the  spectrum  is 


CHROMATIC  ABERRATION.— ACHROMATISM.  71 

permitted  to  fall,  shows  its  color  vividly  where  the  red 
light  falls  upon  it,  but  appears  black  beyond  this  position. 

263.  We  have  thus  far  dealt  with  the  analysis  of  white 
light.     In  reblending  the  constituent  colors,  so  as  to  pro- 
duce the  original,  we  illustrate,  by  synthesis,  the  composi- 
tion of  white  light. 

264.  Let  the  beam  analyzed  be  a  rectangular  slice  of 
light.     By  means  of  a  cylindrical  lens  we  can  recombine 
the  colors,  and  produce  by  their  mixture  the  original  white. 
It  is  also  possible,  by  the  combination  of  the  colors  of  its 
spectrum,  to  build  up  a  perfect  image  of  the  source  of  light. 
The  persistence  of  impressions  on  the  retina  also  offers  a 
ready  means  of  blending  colors. 

Chromatic  Aberration. — Achromatism. 

265.  Owing  to  the  different  refrangibility  of  the  differ- 
ent rays  of  the  spectrum,  it   is  impossible  by  a  single 
spherical  lens  to  bring  them  all  to  a  focus  at  the  same 
point.     The  blue  rays,  for  example,  being  more  refracted 
than  the  red  will  intersect  sooner  than  the  red. 

266.  Hence,  when  a  divergent  cone  of  white  light  is 
rendered  convergent  by  a  lens,  the  convergent  beam,  as  far 
as  the  point  of  intersection  of  the  rays,  will  be  surrounded 
by  a  sheath  of  red  ;  while  beyond  the  focus  the  divergent 
cone  will  be  surrounded  by  a  sheath  of  blue.    Hence,  when 
the  refracted  rays  fall  upon  a  screen  placed  between  the 
lens  and  the  focus  of  blue  rays,  a  white  circle  with  a  red 
border  is  obtained ;  while  if  the  screen  be  placed  beyond 
the  focus  of  red  rays,  the  white  circle  will  have  a  blue 
border.     It  is  impossible  to  produce  a  colorless  image  in 
these  positions  of  the  screen. 

267.  This  lack  of  power  on  the  part  of  a  lens  to  bring  its 
differently-colored  constituents  to  a  common  focus,  is  called 
the  Chromatic  aberration  of  the  lens. 


72  NOTES  ON  LIGHT. 

268.  Newton  considered  it  impossible  to  get  rid  of 
chromatic  aberration  ;  for  he  supposed  the  dispersion  of  a 
prism  or  lens  to  be  proportional  to  its  refraction,  and  that 
if  you  destroyed  the  one  you  destroyed  the  other.     This, 
however,  was  an  error. 

269.  For  two  prisms  producing  the  same  mean  refrac- 
tion may  produce  very  different  degrees  of  dispersion.    By 
diminishing  the  angle  of  the  more  highly-dispersive  prism 
we  can  make  its  dispersion  sensibly  equal  to  that  of  the 
feebly  dispersive  one  ;  and  we  can  neutralize  the  colors  of-, 
both  prisms  by  placing  them  in  opposition  to  each  other, 
without  neutralizing  the  refraction. 

270.  When,  for  example,  a  prism  of  water  is  opposed 
to  a  prism  of  flint-glass,  after  the  dispersion  of  the  water, 
which  is  small,  has  been  destroyed,  the  beam  is  still  re- 
fracted.    If  a  prism  of  crown-glass  be  substituted  for  the 
prism  of  water,  substantially  the  same  effect  is  produced. 
The  flint-glass  is  competent  to  neutralize  the  dispersion  of 
the  crown  before  it  neutralizes  the  refraction. 

271.  What  is  here  said  of  prisms  applies  equally  to 
lenses.     A  convex  crown-glass  lens,  opposed  to  a  concave 
flint-glass  lens,  may  have  its  dispersion  destroyed,  and  still 
images  may  be  formed  by  the  combination  of  the  two 
lenses,  because  of  the  residual  refraction. 

272.  A  combination  of  lenses  wherein  color  is  destroyed 
while  a  certain  amount  of  refraction  is  preserved,  is  called  an 
achromatic  combination,  or  more  briefly  an  achromatic  lens. 

273.  The  human  eye  is  not  achromatic.     It  suffers  from 
chromatic  aberration  as  well  as  from  spherical  aberration. 

Subjective  Colors. 

274.  By  the  action  of  light  the  optic  nerve  is  rendered 
less  sensitive.     When  we  pass  from  bright  daylight  into  a 
moderately-lighted  room,  the  room  appears  dark, 


SUBJECTIVE   COLORS.  73 

275.  This  is  also  true  of  individual  colors;  when  light 
of  any  particular  color  falls  upon  the  eye,  the  optic  nerve 
is  rendered  less  sensitive  to  that  color.     It  is,  in  fact,  par- 
tially blinded  to  its  perception. 

276.  If  the  eyes  be  steadily  fixed  upon  a  red  wafer 
placed  on  white  paper,  after  a  little  time  the  wafer  will  be 
surrounded  by  a  greenish  rim,  and  if  the  wafer  be  moved 
away,  the  place  on  which  it  rested  will  appear  green. 

277.  This  is  thus  explained :  the  eye  by  looking  at  the 
wafer  has  its  sensibility  to  red  light  diminished ;  hence, 
when  the  wafer  is  removed,  the  white  light  falling  upon 
the  spot  of  the  retina  on  which  the  image  of  the  wafer 
rested,  will  have  its  red  constituent  virtually  removed,  and 
will  therefore  appear  of  the  complementary  color.     The 
first  rim  of  green  light  observed  is  due  to  the  extension  of 
the  red  light  of  the  wafer  a  little  beyond  its  geometrical 
image  on  the  retina,  in  consequence  of  the  spherical  aberra- 
tion of 'the  eye. 

278.  Colored  shadows  are  reducible  to  the  same  cause. 
Let  a  strong  red  light,  for  example,  fall  upon  a  white  screen. 
A  body  interposed  between  the  light  and  the  screen  will 
cast  a  shadow,  and  if  this  shadow  be  moderately  illumi- 
nated by  a  second  white  light  it  will  appear  green.   If  the 
original  light  be  blue,  the  shadow  will  appear  yellow ;  if 
the  original  light  be  green,  the  shadow  will  appear  red. 
The  reason  is,  that  the  eye  in  the  first  instance  is  partially 
blinded  to  the  perception  of  the  color  cast  upon  the  screen ; 
hence  the  white  light,  which  reaches  the  eye  from  the 
shadow,  will  have  that  color  partially  withdrawn,  and  the 
shadow  will  appear  of  the  complementary  color. 

279.  Colors  of  this  kind  are  called  subjective  colors  ; 
they  depend  upon  the  condition  of  the  eye,  and  do  not  ex- 
press external  facts  of  color. 

4 


74  NOTES  ON   LIGHT. 

Spectrum  Analysis. 

280.  Metals  and  their  compounds  impart  to  flames  pe- 
culiar colors,  which  are  characteristic  of  the  metals.  Thus 
the  almost  lightless  flame  t>f  a  Bunsen's  burner  is  rendered 
a  brilliant  yellow  by  the  metal  sodium,  or  by  any  vola- 
tilizible  compound  of  that  metal,  such  as  chloride  of  sodium 
or  common  salt.     The  flame  is  rendered  green  by  copper, 
purple  by  zinc,  and  red  by  strontian. 

281.  These  colors  are  due  to  the  vapors  of  the  metals 
which  are  liberated  in  the  flame. 

282.  When  such  incandescent  metallic  vapors  are  ex- 
amined by  the  prism,  it  is  found  that  instead  of  emitting 
rays  which  form  a  continuous  spectrum,  one  color  passing 
gradually  into  another,  they  emit  distinct  groups  of  rays 
of  definite,  but  different  refrangibilities.     The  spectrum 
corresponding  to  these  rays  is  a  series  of  colored  bands, 
separated  from  each  other  by  intervals  of  darkness.    Such 
bands  are  characteristic  of  luminous  gases  of  all  kinds. 

283.  Thus  the  spectrum  of  incandescent  sodium-vapor 
consists  of  a  brilliant  band  on  the  confines  of  the  orange 
and  yellow ;  and  the  vapor  is  incompetent  to  shed  forth 
any  of  the  other  light  of  the  spectrum.     When  this  band 
is  more  accurately  analyzed  it  resolves  itself  into  two  dis- 
tinct bands  ;  greater  delicacy  of  analysis  resolves  it  into  a 
group  of  bands  with  fine  dark  intervals  between  them. 
The  spectrum  of  copper-vapor  is  signalized  by  a  series  of 
green  bands,  while  the  incandescent  vapor  of  zinc  produces 
brilliant  bands  of  blue  and  red. 

284.  The  light   of  the   bands   produced  by  metallic 
vapors  is  very  intense,  the  whole  of  the  light  being  con- 
centrated into  a  few  narrow  strips,  and  escaping  in  a  great 
measure  the  dilution  due  to  dispersion. 

285.  These  colored  bands  are  perfectly  characteristic 


FURTHER  DEFINITION   OF  RADIATION,   ETC.  75 

of  the  vapor ;  from  their  position  and  number  the  sub- 
stance that  produces  them  can  be  unerringly  inferred. 

286.  If  two  or  more  metals  be  introduced  into  the 
flame  at  the  same  time,  prismatic  analysis  reveals  the  bands 
of  each  metal  as  if  the  others  were  not  there.    This  is  also 
true  when  a  mineral  containing  several  metals  is  intro- 
duced into  the  flame.     The  constituent  metals  of  the  min- 
eral will  give  each  its  characteristic  bands. 

287.  Hence,  having  made  ourselves  acquainted  with 
the  bands  produced  by  all  known  metals,  if  entirely  new 
bands  show  themselves,  it  is  a  proof  that  an  entirely  new 
metal  is  present  in  the  flame.     It  is  thus  that  Bunsen  and 
KirchhofF,  the  founders  of  spectrum  analysis,  discovered 
Rubidium  and  Caesium ;  and  that  Thallium,  with  its  superb 
green  band,  was  discovered  by  Mr.  Crookes. 

288.  The  permanent  gases  when  heated  to  a  sufficient 
temperature,  as  they  may  be  by  the  electric  discharge, 
also  exhibit  characteristic  bands  in  their  spectra.     By 
these  bands  they  may  be  recognized,  even  at  stellar  dis- 
tances. 

289.  The  action  of  light  upon  the  eye  is  a  test  of  un,- 
rivalled   delicacy.     In  specti*um  analysis  this   action  is 
brought  specially  into  play;    hence   the   power  of  this 
method  of  analysis.* 

Further  Definition  of  Radiation  and  Absorption. 

290.  The  terms  ray,  radiation,  and  absorption,  were 
employed  long  prior  to  the  views  now  entertained  regard- 

*  Many  persons  are  incompetent  to  distinguish  one  color  of  the  spec- 
trum from  another ;  red  and  green,  for  example,  are  often  confounded. 
Dalton,  the  celebrated  founder  of  the  Atomic  Theory,  could  only  distin- 
guish by  their  form  ripe  red  cherries  from  the  green  leaves  of  the  tree. 
This  point  is  now  attended  to  in  the  choice  of  engine-drivers,  who  have 
to  distinguish  one  colored  signal  from  another.  The  defect  is  called 
color-blindness,  and  sometimes  Daltonism. 


76  NOTES  ON   LIGHT. 

ing  the  nature  of  light.  It  is  necessary  more  clearly  to 
understand  the  meaning  attached  by  the  undulatory  theory 
to  those  terms. 

291.  And  to  complete  our  knowledge  it  is  necessary  to 
know  that  all  bodies,  whether  luminous  or  non-luminous, 
are  radiants ;  if  they  do  not  radiate  light  they  radiate 
heat. 

292.  It  is  also  necessary  to  know  that  luminous  rays 
are  also  heat  rays ;  that  the  self-same  waves  of  ether  falling 
on  a  thermometer  produce  the  effects  of  heat ;  and  im- 
pinging upon  the  retina  produce  the  sensation  of  light. 
The  rays  of  greatest  heat,  however,  as  already  explained, 
lie  entirely  without  the  visible  spectrum. 

293.  The  radiation  both  of  light  and  heat  consists  in 
the  communication  of  motion  from  the  vibrating  atoms 
of  bodies  to  the  ether  which  surrounds  them.     The  ab- 
sorption of  heat  consists  in  the  acceptance  of  motion,  on 
the  part  of  the  atoms  of  a  body,  from  ether  which  has  been 
already  agitated  by  a  source  of  light  or  heat.     In  radia- 
tion, then,  motion  is  yielded  to  the  ether ;  in  absorption, 
motion  is  received  from  the  ether. 

294.  When  a  ray  of  light  or  of  heat  passes  through  a 
body  without  loss ;  in  other  words,  when  the  waves  are 
transmitted  through  the  ether  which  surrounds  the  atoms 
of  the  body,  without  sensibly  imparting  motion  to  the 
atoms  themselves,  the  body  is  transparent.     If  motion  be 
in  any  degree  transferred  from  the  ether  to  the  atoms,  in 
that  degree  is  the  body  opaque. 

295.  If  either  light  or  radiant  heat  be  absorbed,  the 
absorbing  body  is  ic armed /  if  no  absorption  takes  place, 
the  light  or  radiant  heat,  whatever  its  intensity  may  be, 
passes  through  the  body  without  affecting  its  tempera- 
ture. 

296.  Thus  in  the  dark  foci  referred  to  in  Note  246,  or 


THE  PURE  SPECTRUM:    FRAUXHOFER'S  LINES.         77 

in  the  focus  of  the  most  powerful  burning  mirror  which 
concentrates  the  beams  of  the  sun,  the  air  might  be  of  a 
freezing  temperature,  because  the  absorption  of  the  heat 
by  the  air  is  insensible.  A  plate  of  clear  rock-salt,  more- 
over, placed  at  the  focus,  is  scarcely  sensibly  heated,  the 
absorption  being  small ;  while  a  plate  of  glass  is  shivered, 
and  a  plate  of  blackened  platinum  raised  to  a  white  heat, 
or  even  fused,  because  of  their  powers  of  absorption. 

297.  It  is  here  worth  remarking  that  calculations  of 
the  temperatures  of  comets,  founded  on  their  distances 
from  the  sun>  may  be,  and  probably  are,  entirely  fal- 
lacious.    The  comet,  even  when  nearest  to  the  sun,  might 
be   intensely   cold.      It   might   carry  with  it  round  its 
perihelion  the  chill  of  the  most  distant  regions  of  space. 
If  transparent  to  the  solar  rays  it  would  be  unaffected 
by  the  solar  heat,  as  long  as  that  heat  maintained  the 
radiant  form. 

The  Pure  Spectrum :  Fraunhofer^  s  Lines. 

298.  When  a  beam  of  white  light  issuing  from  a  slit  is 
decomposed,  the  spectrum  really  consists  of  a  series  of 
colored  images  of  the  slit  placed  side  by  side.     If  the  slit 
be  wide,  these  images  overlap  •  but  in  a  pure  spectrum 
the  colors  must  not  overlap  each  other. 

299.  A  pure  spectrum  is  obtained  by  making  the  slit 
through  which  the  decomposed  beam  passes  very  narrow, 
and  by  sending  the  beam  through  several  prisms  in  suc- 
cession, thus  augmenting  the  dispersion. 

300.  When  the  light  of  the  sun  is  thus  treated,  the 
solar  spectrum  is  found  to  be  not  perfectly  continuous ; 
across  it  are  drawn  innumerable  dark  lines,  the  rays  cor- 
responding to  which  are  absent.     Dr.  Wollaston  was  the 
first  to  observe  some  of  these  lines.     They  were  afterward 
studied  with  supreme  skill  by  Fraunhofer,  who  lettered 


78  NOTES  ON  LIGHT. 

them  and  made  accurate  maps  of  them,  and  from  him  they 
have  been  called  Fraunhofer^  s  lines. 

Reciprocity  of  Radiation  and  Absorption. 

301.  To  account  for  the  missing  rays  of  the  lines  of 
Fraunhofer  was  long  an  enigma  with  philosophers.     By 
the  genius  of  Kirchhoff  the  enigma  was  solved.     Its  solu- 
tion carried  with  it  a  new  theory  of  the  constitution  of  the 
sun,  and  a  demonstration  of  a  method  which  enables  us 
to  determine  the  chemical  composition  of  the  sun,  the 
stars,  and  the  nebulae.     The  application  of  Kirchhoff's 
principles  by  Messrs.  Huggins,  Miller,  Secchi,  Janssen, 
and  Lockyer,  has  been  of  especial  interest  and  importance. 

302.  Kirchhoff's  explanation  of  the  lines  of  Fraunhofer 
is  based  upon  the  principle  that  every  body  is  specially 
opaque  to  such  rays  as  it  can  itself  emit  when  rendered 
incandescent. 

303.  Thus  the  radiation  from  a  carbonic-oxide  flame, 
which  contains  carbonic  acid  at  a  high  temparature,  is  in- 
tercepted in  an  astonishing  degree  by  carbonic  acid.     If 
the  rays  from  a  sodium  flame  be  sent  through  a  second 
sodium  flame,  they  will  be  stopped  with  particular  energy 
by  the  second  flame.     The  rays  from  incandescent  thal- 
lium vapor  are  intercepted  by  thallium  vapor,  those  from 
lithium  vapor    by  lithium  vapor,  and  so   of   the  other 
metals. 

304.  In  the  language  of  the  undulatory  theory,  waves 
of  ether  are  absorbed  with  special  energy — their  motion  is 
taken  up  with  special  facility — by  atoms  whose  periods  of 
vibration  synchronize  with  the  periods  of  the  waves.    This 
is  another  way  of  stating  that  a  body  absorbs  with  special 
energy  the  rays  which  it  can  itself  emit. 

305.  If  a  beam  of  white  light  be  sent  through  the  in- 
tensely yellow  flame  of  sodium  vapor,  the  yellow  con- 


RECIPROCITY   OF  RADIATION  AND  ABSORPTION.       79 

stituent  of  the  beam  is  intercepted  by  the  flame,  while 
rays  of  other  refrangibilities  are  allowed  free  transmission. 

306.  Hence,  when  the  spectrum  of  the  electric  light  is 
thrown  upon  a  white  screen,  the  introduction  of  a  sodium 
flame  into  the  path  of  the  rays  cuts  off  the  yellow  compo- 
nent of  the  light,  and  the  spectrum  is  furrowed  by  a  dark 
band  in  place  of  the  yellow. 

307.  Introducing  other  flames  in  the  same  manner  in 
the  path  of  the  beam,  if  the  quantity  of  metallic  vapor  in 
the  flame  be  sufficient,  each  flame  will  cut  out  its  own  bands. 
And  if  the  flame  through  which  the  light  passes  contain 
the  vapors  of  several  metals,  we  shall  have  the  dark  char- 
acteristic bands  of  all  of  them  upon  the  screen. 

308.  Expanding  in  idea  our  electric  light  until  it  forms 
a  globe  equal  to  the  sun  in  size,  and  wrapping  round  this 
incandescent  globe  an  atmosphere  of  flame,  that  atmos- 
phere would  cut  off  those  rays  of  the  globe  which  it  can 
itself  emit,  the  interception  of  the  rays  being  declared  by 
dark  lines  in  the  spectrum. 

309.  We  thus  arrive  at  a  complete  explanation  of  the 
lines  of  Fraunhofer,  and  a  new  theory  of  the  constitution 
of  the  sun.     The  orb  consists  of  a  solid  or  molten  nucleus, 
in  a  condition  of  intense  incandescence,  but  it  is  sur- 
rounded  by   a  gaseous   photosphere    containing  vapors 
which  absorb  those  rays  of  the  nucleus  which  they  them- 
selves emit.     The  lines  of  Fraunhofer  are  thus  produced. 

310.  The  lines  of  Fraunhofer  are  narrow  bands  of 
partial  darkness ;  they  are  really  illuminated  by  the  light 
of  the  gaseous  envelope  of  the  sun.     But  this  is  so  feeble 
in  comparison  with  the  light  of  the  nucleus  intercepted  by 
the  envelope,  that  the  bands  appear  dark  in  comparison 
with  the  adjacent  brilliance. 

311.  Were  the  central  nucleus  abolished,  the  bands 
of  Fraunhofer  on  a  perfectly  darlt  ground  would  be  trans- 


80  NOTES  ON  LIGHT. 

formed  into  a  series  of  bright  bands.  These  would  re- 
semble the  spectra  obtained  from  a  flame  charged  with 
metallic  vapors.  They  would  constitute  the  spectrum  of 
the  solar  atmosphere. 

312.  It  is  not  necessary  that  the  photosphere  should 
be  composed  of  pure  vapor.     Doubtless  it  contains  vast 
masses  of  incandescent  cloudy  matter,  composed  of  white 
hot  molten  particles.     These  intensely  luminous  white  hot 
clouds  may  be  the  main  origin  of  the  light  which  the  earth 
receives  from  the  sun,  and  with  them  the  true  vapor  of  the 
photosphere  may  be  more  or  less  confusedly  mingled.    But 
the  vapor  which  produces  the  lines  of  Fraunhofer  musjb 
exist  outside  the  clouds,  as  assumed  by  Kirchhoff. 

Solar  Chemistry. 

313.  From  the  dark  bands  of  the  spectrum  we  can  de- 
termine what  substances  enter  into  the  composition  of  the 
solar  atmosphere. 

314.  One  example  will  illustrate  the  possibility  of  this. 
Lot  the  light  from  the  sun  and  the  light  from  incandes- 
cent sodium  vapor  pass  side  by  side  through  the  same  slit, 
and  be  decomposed  by  the  same  prism.     The  solar  light 
will  produce  its  spectrum,  and  the  sodium  light  its  yellow 
band.     This  yellow  band  will  coincide  exactly  in  position 
with  a  characteristic  dark  band  of  the  solar  spectrum, 
which  Fraunhofer  distinguishes  by  the  letter  r>. 

315.  Were  the  solar  nucleus  absent,  and  did  the  va- 
porous photosphere  alone  emit  light,  the  dark  line  D  would 
be  a  bright  one.     Its  character  and  position  prove  it  to  be 
the  light  emitted  by  sodium.     This  metal,  therefore,  is 
contained  in  the  atmosphere  of  the  sun.* 

*  By  reference  to  note  283  it  will  be  seen  that  the  sodium  line  is 
resolved  by  delicate  analysis  into  a  group  of  lines.  The  Fraunhofer 
dark  band  D  is  similarly  resolved.  It  ought  to  be  mentioned  that  both 


PLANETARY   CHEMISTRY.  81 

316.  The  result  is  still  more  convincing  when  a  metal 
which  gives  a  numerous  series  of  bright  bands  finds  each 
of  its  bands  exactly  coincident  with  a  dark  band  of  the 
solar  spectrum.     By  this  method  Kirchhoff,  to  whom  we 
owe,  in  all  its  completeness,  this  splendid  generalization, 
established  the  existence  of  iron,  calcium,  magnesium, 
sodium,  chromium,  and  other  metals,  in  the  solar  atmos- 
phere ;  and  Mr.  Huggins  has  extended  the  application  of 
the  method  to  the  light  of  the  planets,  fixed  stars,  and 
nebulas.* 

Planetary  Chemistry. 

317.  The  light  reflected  from  the  moon  and  planets  is 
solar  light ;  and,  if  unaffected  by  the  planet's  atmosphere, 
the  spectrum  of  the  planet  would  show  the  same  lines  as 
the  solar  spectrum. 

318.  The  light  of  the  moon  shows  no  other  lines.   There 
is  no  evidence  of  an  atmosphere  round  the  moon. 

319.  The  lines  in  the  spectrum  of  Jupiter  indicate  a 
powerful  absorption  by  the  atmosphere  of  this  planet.  The 
atmosphere  of  Jupiter  contains  some  of  the  gases  or  vapors 
present  in  the  earth's  atmosphere.     Feeble  lines,  some  of 
them  identical  with  those  of  Jupiter,  occur  in  the  spectrum 
of  Saturn. 

320.  The  lines  characterizing  the  atmospheres  of  Jupiter 
and  Saturn  are  not  present  in  the  spectrum  of  Mars.     The 
blue  portion  of  the  spectrum  is  mainly  the  seat  of  absorp- 
tion ;  and  this,  by  giving  predominance  to  the  red  rays, 
may  be  the  cause  of  the  red  color  of  Mars. 

321.  All  the  stronger  lines  of  the  solar  spectrum  are 
found  in  the  spectrum  of  Venus,  but  no  additional  lines. 

Mr.  Talbot  and  Sir  John  Herschel  clearly  foresaw  the  possibility  of  em- 
ploying spectrum  analysis  in  detecting  minute  traces  of  bodies. 

*  Prof.  Stokes  foresaw  the  possible  application  of  spectrum  analysis 
to  solar  chemistry. 


82  NOTES  OX   LIGHT. 

Stellar  Chemistry. 

822.  The  atmosphere  of  the  star  Aldebaran  contains 
hydrogen,  sodium,  magnesium,  calcium,  iron,  bismuth, 
tellurium,  antimony,  mercury.  The  atmosphere  of  the  star 
Alpha  in  Orion  contains  sodium,  magnesium,  calcium, 
iron,  and  bismuth. 

323.  No  star  sufficiently  bright  to  give  a  spectrum  has 
been  observed  to  be  without  lines.     Star  differs  from  star 
only  in  the  grouping  and  arrangement  of  the  numerous 
fine  lines  by  which  their  spectra  are  crossed. 

324.  The  dark  absorption  lines  are  strongest  in  the 
spectra  of  yellow  and  red  stars.     In  white  stars  the  lines, 
though  equally  numerous,  are  very  poor  and  faint. 

325.  A  comparison  of  the  spectra  of  stars  of  different 
colors  suggests  that  the  colors  of  the  stars  may  be  due  to 
the  action  of  their  atmospheres.     Those  constituents  of  the 
white  light  of  the  star  on  which  the  lines  of  absorption  fall 
thickest  are  subdued,  the  star  being  tinted  by  the  residual 
color. 

Father  Secchi,  of  Rome,  has  studied  the  light  of  many 
hundreds  of  stars,  and  has  divided  them  into  four  classes. 

Nebular  Chemistry. 

326.  Some  nebula3  give  spectra  of  bright  bands,  others 
give  continuous  spectra.     The  light  from  the  former  ema- 
nates from  intensely  heated  matter  existing  in  a  state  of 
gas.     This  may  in  part  account  for  the  weakness  of  the 
light  of  these  nebula?. 

327.  It  is  probable  that  two  of  the  constituents  of  the 
gaseous  nebulae  are  hydrogen  and  nitrogen. 

The  Red  Prominences  and  Envelope  of  the  Sun. 

328.  Astronomers  had  observed  during  total  eclipses 
of  the  sun  vast  red  prominences  extending  from  the  solar 


THE  RED  PROMINENCES  OF  THE   SUN.  83 

.  limb  many  thousand  miles  into  space.  The  intense  illumi- 
nation of  the  circumsolar  region  of  our  atmosphere  masks, 
under  ordinary  circumstances,  the  red  prominences.  They 
are  quenched,  as  it  were,  by  excess  of  light. 

329.  But  when,  by  the  intervention  of  the  dark  body 
of  the  moon,  this  light  is  cut  off,  the  prominences  are  dis- 
tinctly seen. 

330.  It  was    proved  by  Mr.  De  la  Hue   and    others 
that  the  red  matter  of  the  prominences  was  wrapped  round 
a  large  portion  of  the  sun's  surface.     According  to  the 
observations  of  Mr.  Lockyer,  the  red  matter  forms  a  com- 
plete envelope  round  the  sun. 

331.  Examined  by  the  spectroscope  the  matter  of  the 
prominences  shows  itself  to  be,  for  the  most  part,  incan- 
descent hydrogen.   With  it  are  mixed  the  vapors  of  sodium 
and  magnesium. 

332.  Mr.  Janssen,  in  India,  and  Mr.  Lockyer  subse- 
quently, but  independently,  in  England,  proved  that  the 
bright  bands  of  the  prominences  might  be  seen  without 
the  aid  of  a  total  eclipse.     The  explanation  of  this  dis- 
covery is  glanced  at  in  Note  284,  where  the  intensity  of 
the  bright  bands  of  incandescent  gases  was  referred  to  the 
practical  absence  of  dispersion. 

333.  By  sending  the  light,  which  under  ordinary  cir- 
cumstances masks  the  hydrogen  bands,  through  a  sufficient 
number  of  prisms,  it  may  be  dispersed,  and  thereby  en- 
feebled in  any  required  degree.      When  sufficiently  en- 
feebled the  undispersed  light  of  the  incandescent  hydrogen 
dominates  over  that  of  the  continuous  spectrum.   By  going 
completely  round  the  periphery  of  the  sun  Mr.  Lockyer 
found  this  hydrogen  atmosphere  everywhere  present,  its 
depth,  generally  about  5,000  miles,  being  indicated  by  the 
length   of    its   characteristic   bright   lines.      Where  the 
hydrogen  ocean  is  shallow,  the  bright  bands  are  short ; 


J^ 


84  NOTES  ON  LIGHT. 

where  the  prominences  rise  like  vast  waves  above  the  level 
of  the  ocean,  the  bright  lines  are  long.  The  prominences 
sometimes  reach  a  height  of  70,000  miles. 

The  Rainbow. 

334.  A  beam  of  solar  light,  falling  obliquely  on  the 
surface  of  a  rain-drop,  is  refracted  on  entering  the  drop ; 
it  is  in  part  reflected  at  the  back  of  the  drop,  and  on 
emerging  from  the  drop  it  is  again  refracted. 

335.  By   these   two   refractions    on   entrance   and  on 
emergence  the  beam  of  light  is  decomposed,  and  it  quits 
the  drop  resolved  into  its  colored  constituents.     It  is  re- 
ceived by  the  eye  of  an  observer  who  faces  the  drop  and 
turns  his  back  to  the  sun. 

336.  In  general  the  solar  rays,  when  they  quit  the  drop, 
are  divergent,  and  therefore  produce  but  a  feeble  effect 
upon  the  eye.     But  at  one  particular  angle  the  rays,  after 
having  been  twice  refracted  and  once  reflected,  issue  from 
the  drop  almost  perfectly  parallel.     They  thus  preserve 
their  intensity  like  rays  reflected  from  a  parabolic  mirror, 
and  produce  a  corresponding  effect  upon  the  eye.     The 
angle  at  which  this  parallelism  is  established  varies  with 
the  refrangibility  of  the  light. 

337.  Draw  a  line  from  the  sun  to  the  observer's  eye 
and  prolong  this  line  beyond  the  observer.     Conceive  an- 
other line  drawn  from  the  eye  enclosing  an  angle  of  42° 
30'  with  the  line  drawn  to  the  sun.     The  rain-drop  struck 
by  this  second  line  will  send  to  the  eye  a  parallel  beam  of 
red  light.     Every  other  drop  similarly  situated,  that  is  to 
say,  every  drop  at  an  angular  distance  of  42°  30'  from  the 
line  drawn  to  the  sun,  will  do  the  same.     We  thus  obtain 
a  circular  hand  of  red  light,  forming  part  of  the  base  of  a 
cone,  by  which  the  eye  of  the  observer  is  the  apex.   Because 


THE  RAINBOW.  85 

of  the  angular  magnitude  of  the  sun  the  width  of  this  band 
will  be  half  a  degree. 

338.  From  the  eye  of  the  observer  conceive  another 
line  to  be  drawn  enclosing  an  angle  of  40°  30'  with  the  line 
drawn  to  the  sun.     A  drop  struck  by  this  line  will  send 
along  the  line  an  almost  perfectly  parallel  beam  of  violet 
light  to  the  eye.     All  drops  at  the  same  angular  distance 
will  do  the  same,  and  we  shall  obtain  a  band  of  violet 
light  of  the  same  width  as  the  red.     These  two  bands  con- 
stitute the  limiting  colors  of  the  rainbow,  and  between 
them  the  bands  corresponding  to  the  other  colors  lie. 

339.  The  rainbow  is  in  fact  a  spectrum,  in  which  the 
rain-drops  play  the  part  of  prisms.     The  width  of  the  bow 
from  red  to  violet  is  about  two  degrees.     The  size  of  the 
arc  visible  at  any  time  manifestly  depends  upon  the  posi- 
tion of  the  sun.     The  bow  is  grandest  when  it  is  formed 
by  the  rising  or  the  setting  sun.     An  entire  semicircle  is 
then  seen  by  an  observer  on  a  plain,  while  from  a  mountain- 
top  a  still  greater  arc  is  visible. 

340.  The  angular  distances  and  the  order  of  colors  here 
given  correspond  to  the  primary  bow,  but  in  addition  to 
this  we  usually  see  a  secondary  bow  of  weaker  hues,  and 
in  which  the  order  of  the  colors  is  that  of  the  primary  in- 
verted.    In  the  primary  the  red  band  forms  the  convex 
surface  of  the  arch  ;  it  is  the  largest  band ;  in  the  second- 
ary the  violet  band  is  outside,  the  red  forming  the  con- 
cavity of  the  bow. 

341.  The  secondary  bow  is  produced  by  rays  which 
have  undergone  two  reflections  within  the  drop,  as  well  as 
two  refractions  at  its  surface.     It  is  this  double  internal 
reflection  that  weakens  the  color.     In  the  primary  bow  the 
incident  rays  strike  the  upper  hemisphere  of  the  drop,  and 
emerge  from  the  lower  one  ;  in  the  secondary  bow  the  in- 
cident rays  strike  the  lower  hemisphere  of  the  drop,  emerge 


86  NOTES  ON  LIGHT. 

from  the  upper  one,  and  then  cross  the  incident  rays  to 
reach  the  eye  of  the  observer.  The  secondary  bow  is  3^ 
degrees  wide,  and  it  is  7 1  degrees  higher  than  the  primary. 
From  the  space  between  the  two  bows  part  of  the  light 
reflected  from  the  anterior  surfaces  of  the  rain-drops 
reaches  the  eye ;  but  no  light  whatever  that  enters  the 
rain-drops  in  this  space  is  reflected  to  the  eye.  Hence  this 
region  of  the  falling  shower  is  darkest. 

Interference  of  Light. 

342.  In  wave-motion  we  must  clearly  distinguish  the 
motion  of  the  wave  from,  the  motion  of  the  individual  par- 
ticles which  at  any  moment  constitute   the  wave.     For 
while  the  wave  moves  forward  through  great  distances, 
the  individual  particles  of  water  concerned  in  its  propaga- 
tion perform  a  comparatively  short  excursion  to  and  fro. 
A  sea-fowl,  for  example,  as  the  waves  pass  it,  is  not  car- 
ried forward,  but  moves  up  and  down.* 

343.  Here,  as  in  other  cases,   the   distance   through 
which  the  individual  water"  particles  oscillate,  or  through 
which  the  fowl  moves  vertically  up  and  down,  is  called 
the  amplitude  of  the  oscillation. 

344.  When  light  from,  two   different   sources   passes 
through  the  same  ether,  the  waves  from  the  one  source 
must  be  more  or  less  affected  by  the  waves  from  the  other. 
This  action  is  most  easily  illustrated  by  reference  to  water- 
waves. 

345.  Let  two  stones  be  cast  at  the  same  moment  into 
still  water.     Round  each  of  them  will  spread  a  series  of 
circular  waves.     Let  us  fix  our  attention  on  a  point  A  in 
the  water,  equally  distant  from  the  two  centres  of  disturb- 
ance.    The  first  two  crests  of  both  systems  of  waves  reach 

-_.- '•*  Strictly  speaking,  the  water  particles  .describe  closed  curves,  and  not 
straight  vertical  lines. 


INTERFERENCE  OF  LIGHT.  87 

this  point  at  the  same  moment,  and  it  is  lifted  by  their 
joint  action  to  twice  the  height  that  it  would  attain  through 
the  action  of  either  wave  taken  singly. 

346.  The  first  depression,  or  sinus  as  it  is  called,  of  the 
one  system  of  waves  also  reaches  the  point  A  at  the  same 
moment  as  the  first  sinus  of  the  other,  and  through  their 
joint  action  the  point  is  depressed  to  twice  the  depth  that 
it  would  attain  l)y  the  action  of  either  sinus  taken  singly. 

347.  What  is  true  of  the  first  crest  and  the  first  de- 
pression is  also  true  of  all  the  succeeding  ones.     At  the 
point  A  the  successive  crests  will  coincide,  and  the  suc- 
cessive depressions  will  coincide,  the  agitation  of  the  point 
being  twice  what  it  would  be  if  acted  upon  by  one  only  of 
the  systems  of  waves. 

348.  The  length  of  a  wave  is  the  distance  from  any 
crest,  or  any  sinus,  to  the  crest  or  sinus  next  preceding  or 
succeeding.     In  the  case  of  the  two  stones  dropped  at  the 
same  moment  into  still  water,  it  is  manifest  that  the  coin- 
cidence of  crest  with  crest  and  of  sinus  with  sinus  would 
also  take  place  if  the  distance  from  the  one  stone  to  the 
point  A  exceeded  the  distance  of  the  other  stone  from  the 
same  point  by  a  whole  wave-length.     The  only  difference 
would  be,  that  the  second  wave  of  the  nearest  stone  would 
then  coincide  with  the  first  wave  of  the  most  distant  one. 
The  one  system  of  waves  would  here  be  retarded  a  whole 
wave-length  behind  the  other  system. 

349.  A  little  reflection  will  also  make  it  clear  that 
coincidence  of  crest  with  crest  and  of  sinus  with  sinus  will 
also  occur  at  the  point  A  when  the  retardation  of  the  one 
system  behind  the  other  amounts  to  any  number  of  ichole 
wave-lengths. 

350.  But  if  we  suppose  the  point  A  to  be  half  a  wave- 
length more  distant  from  the  one  stone  than  from  the 
other,  then  as  the  waves  pass  the  point  A  the  crests  of  one 


88  NOTES  ON   LIGHT. 

of  the  systems  will  always  coincide  with  the  sinuses  of  the 
other.  When  a  wave  of  the  one  system  tends  to  elevate 
the  point  A,  a  wave  from  the  other  system  will,  at  the 
same  moment,  tend  to  depress  it.  As  a  consequence  the 
point  will  neither  rise  nor  sink,  as  it  would  do  if  acted 
upon  by  either  system  of  waves  taken  singly.  The  same 
neutralization  of  motion  occurs  where  the  difference  of  path 
between  the  two  stones  and  the  point  A  amounts  to  any 
odd  number  of  half  wave-lengths. 

351.  Here,  then,  by  adding  motion  to  motion,  we  abolish 
motion  and  produce  rest.     In  precisely  the  same  way  we 
can,  by  adding  sound  to  sound,  produce  silence,  one  sys- 
tem of  sound-waves  being  caused  to  neutralize  another. 
So  also  by  adding  heat  to  heat  we  can  produce  cold,  while 
by  adding  light  to  light  we  can  produce  darkness.     It  is 
this  perfect  identity  of  the  deportment  of  light  and  radiant 
heat  with  the  phenomena  of  wave-motion  that  constitutes 
the  strength  of  tlie  Theory  of  Undulation. 

352.  This  action  of  one  system  of  waves  upon  another, 
whereby  the  oscillatory  motion  is  either  augmented  or 
diminished,  is  called  Interference.     In  relation  to  optical 
phenomena  it  is  called  the  Interference  of  Light.     We 
shall  henceforth   have   frequent   occasion  to   apply  this 
principle. 

Diffraction,  or  the  Inflection  of  Light. 

353.  Newton,  who  was  familiar  with  the  idea  of  an 
ether,  and   indeed  introduced  it  in  some  of  his  specula- 
tions, objected  that  if  light  were  propagated  by  waves, 
shadows  could  not  exist ;  for  that  the  waves  would  bend 
round  opaque  bodies,  and   abolish  the   shadows  behind 
them.     According  to  the  wave  theory  this  bending  round 
of  the  wraves  actually  occurs,  but  the  different  portions 


DIFFRACTION,   OR   THE  INFLECTION   OF  LIGHT.        §9 

of  the  inflected  waves  destroy  each  other  'by  their  inter- 
ference. 

354.  This  bending  of  the  waves  of  light  round  the  edges 
of  opaque  bodies,  receives  the  name  of  Diffraction  or  In- 
flection (German,  Beugung).     We  have  now  to  consiclef 
some  of  the  effects  of  diffraction. 

355.  And  for  this  purpose  it  is  necessary  that  our  source 
of  light  should  be  a  physical  point  or  a  fine  line :  for  when 
an  extensive  luminous  surface  is  employed,  the  effects  of 
its  different  points  in  diffraction  phenomena  neutralize 
each  other. 

356.  A. point  of  light  may  be  obtained  by  converging, 
by  a  lens  of  short  focus,  the  parallel  rays  of  the  sun, 
admitted  through  a  small  aperture   into  a  dark  room. 
The  small  image  of  the  sun  formed  at  the  focus  is  here 
our  luminous  point.     The  image  of  the  sun  formed  on  the 
surface  of  a  silvered  bead,  or  indeed  upon  the  convex  fur- 
face  of  a  glass  lens,  or  of  a  watch-glass  blackened  within, 
also  answers  the  purpose. 

357.  A  line  of  light  is  obtained  by  admitting  the  sun- 
light through  a  slit,  and  sending  the  slice  of  light  through 
a  cylindrical  lens.     The  rectangular  beam  is  contracted 
to  a  physical  line  at  the  focus  of  the  lens.     A  glass  tube 
blackened  within  and  placed  in  the  light,  reflects  from  its 
surface  a  luminous  line  which  also  answers  the  purpose. 
For  many  experiments,  indeed,  the  circular  aperture,  or 
the   slit  itself,  suffices  without   any  condensation   by  a 
lens. 

358.  In  the  experiment  now  to  be  described,  a  slit  of 
variable  width  is  placed  in  front  of  the  electric  lamp,  and 
this  slit  is  looked  at  from  a  distance  through  another  slit, 
also  of  variable  aperture.     The  light  of  the  lamp  is  ren- 
dered monochromatic  by  placing  a  pure  red  glass  in  front 
of  the  slit. 


90  NOTES  ON  LIGHT. 

359.  With  the  eye  placed  in  the  straight  line  drawn 
through  both  slits  from  the  incandescent  carbon  points  of 
the  electric  lamp  an  extraordinary  appearance  is  observed. 
Firstly,  the  slit  in  front  of  the  lamp  is  seen  as  a  vivid 
rectangle  of  light ;  but  right  and  left  of  it  is  a  long  series 
of  rectangles,  decreasing  in  vividness,  and  separated  from 
each  other  by  intervals  of  absolute  darkness. 

360.  The  breadth  of  the  bands  varies  with  the  width 
of  the  slit  placed  in  front  of  the  eye.    If  the  slit  be  widened, 
the  images  become  narrower,  and  crowd  more  closely  to- 
gether; if  the  slit  be  narrowed,  the  images  widen  and 
retreat  from  each  other. 

361.  It  may  be  proved  that  the  width  of  the  bands  is 
inversely  proportional  to  the  width  of  the  slit  held  in  front 
of  the  eye. 

362.  Leaving  every  thing  else  unchanged,  let  a  blue 
glass  or  a  solution  of  ammonia  sulphate  of  copper,  which 
gives  a  very  pure  blue,  be  placed  in  the  path  of  the  light. 
A  series  of  blue  bands  is  thus  obtained,  exactly  like  the 
former  in  all  respects  save  one;  the  blue  rectangles  are 
narrower^  and  they  are  closer  together,  than  the  red  ones. 

363.  If  we  employ  colors  of  intermediate  refrangibili- 
ties  between  red  and  blue,  which  we  may  do  by  causing 
the  different  colors  of  a  spectrum  to  shine  through  the  slit, 
we  should  obtain  bands  of  color  intermediate  in  width  and 
occupying  intermediate  positions  between  those  of  the  red 
and  blue.     Hence  when  white  light  passes  through  the  slit 
the  various  colors  are  not  superposed,  and  instead  of  a 
series  of  monochromatic  bands,  separated  from  each  other 
by  intervals  of  darkness,  we  have  a  series  of  colored  spec- 
tra placed  side  by  side,  the  most  refrangible  color  of  each 
spectrum  being  nearest  to  the  slit. 

364.  When  the  slit  in  front  of  the  camera  is  illuminated 
by  a  candle-flame,  instead  of  the  more  intense  electric  light, 


DIFFRACTION,   OR  THE  INFLECTION   OF  LIGHT.        01 

substantially  the  same  effects,  though  less  brilliant,  are 
observed. 

365.  What  is  the  meaning  of  this  experiment,  and  how 
are  the  lateral  images  of  the  slit  produced  ?     Of  these  and 
certain  accompanying  results  the  emission  theory  is  in- 
competent to  offer  any  explanation.     Let  us  see  how  they 
are  accounted  for  by  the  theory  of  undulation. 

366.  For  the  sake  of  simplicity,  we  will  consider  the 
case  of  monochromatic  light.     Conceive  a  wave  of  ether 
advancing  from  the  first  slit  toward  the  second,  and  finally 
filling  the  second  slit.     When  the  wave  passes  through 
the  latter  it  not  only  pursues  its  direct  course  to  the 
retina,  but  diverges  right  and  left,  tending  to  throw  into 
motion  the  entire  mass  of  the  ether  behind  the  slit.     In 
fact,  every  point  of  the  wave  which  Jills  the  slit  is  itself  a 
centre  of  new  wave-systems,  which  are  transmitted  in  all 
directions  through  the  ether  behind  the  slit.      We  have 
now  to  examine  how  these  secondary  waves  act  upon  each 
other. 

367.  First,  let  us  regard  the  central  rectangle  of  the 
series.     It  is  manifest  that  the  different  parts  of  every 
transverse  section  of  the  wave,  which  in  this  case  fills  our 
slit,  reach  the  retina  at  the  same  moment.     They  are  in 
complete  accordance,  for  no  one  portion  is  retarded  in 
reference  to  any  other  portion.     The  rays  thus  coming 
direct  from  the  source  through  the  slit  to  the  retina  pro- 
duce the  central  band  of  the  series. 

368.  But  now  let  us  consider  those  waves  which  diverse 

O 

obliquely  from  the  slit.  In  this  case,  the  waves  from  the 
two  edges  of  the  slit  have,  in  order  to  reach  the  retina,  to 
pass  over  unequal  distances.  Let  us  suppose  the  differ- 
ence in  path  of  the  two  marginal  rays  to  be  a  whole  wave- 
length of  the  red  light ;  how  must  this  difference  affect  the 
final  illumination  of  the  retina  ? 


92  NOTES  ON  LIGHT. 

369.  Fix  your  attention  upon  the  particular  ray  or  line 
of  light  that  passes  exactly  through  the  centre  of  the  slit  to 
the  retina.     The  difference  of  path  between  this  central 
ray  and  the  two  marginal  rays  is,  in  the  case  here  sup- 
posed, half  a  wave-length.     The  least  reflection  will  make 
it  clear  that  every  ray  on  the  one  side  of  the  central  liue 
finds  a  ray  upon  the  other  side,  from  which  its  path  differs 
by  half  an  undulation,  with  which,  therefore,  it  is  in  com- 
plete discordance.     The  consequence  is  that  the  light  on 
the  one  side  of  the  central  line  will  completely  abolish  the 
light  on  the  other  side  of  that  line,  absolute  darkness  be- 
ing the  result  of  their  mutual  extinction.     The  first  darJc 
interval  of  our  series  of  bands  is  thus  accounted  for.     It 
is  produced  by  an  obliquity  which  causes  the  paths  of  the 
marginal  rays  to  be  a  whole  wave-length  different  from 
each  other. 

370.  When  the  difference  between  the  paths  of  the 
marginal  rays  is  half  a  wave-length^  a  partial  destruction 
of  the  light  is  effected.      The  luminous  intensity  corre- 
sponding to  this  obliquity  is  a  little  less  than  one-half— 
accurately  0.4 — of  that  of  the  undiffracted  light. 

371.  If  the  paths  of  the  marginal  rays  be  three  semi-\ 
undulations  different  from  each  other,  and  if  the  whole 
beam  be  divided  into  three  equal  parts,  two  of  these  parts 
will  completely  neutralize  each  other,  the  third  only  being 
effective.     Corresponding,  therefore,  to  an  obliquity  which 
produces  a  difference  of  three   semi-undulations   in  the 
marginal  rays,  we  have  a  luminous  band,  but  one  of 
considerably  less  intensity  than  the  undiffracted  central 
band. 

372.  With  a  marginal  difference  of  path  of  four  semi- 
undulations  we  have  a  second  extinction  of  the  entire 
beam,  a  space  of  absolute  darkness  corresponding  to  this 
obliquity.     In  this  way  we  might  proceed  further,  the 


MEASUREMENT  OF  THE  WAVES   OF  LIGHT.  93 

general  result  being  that,  whenever  the  obliquity  is  such 
as  to  produce  a  marginal  difference  of  path  of  an  even 
number  of  semi-undulations,  we  have  complete  extinction ; 
while,  when  the  marginal  difference  is  an  odd  number  of 
semi-undulations,  we  have  only  partial  extinction,  a  por- 
tion of  the  beam  remaining  as  a  luminous  band. 

373.  A  moment's  reflection  will  make  it  plain  that  the 
shorter  the  wave,  the  less  will  be  the  obliquity  required 
to  produce  the  necessary  retardation.     The  maxima  and 
minima  of  blue  light  must,  therefore,  fall  nearer  to  the 
centre  than  the  maxima  and  minima  of  red  light.     The 
maxima  and  minima  of  the  other  colors  fall  between  these 
extremes.     In  this  simple  way  the  undulatory  theory  com- 
pletely accounts  for  the  extraordinary  appearance  referred 
to  in  Note  359.     When  a  slit  and  telescope  are  used,  in- 
stead of  the  slit  and  naked  eye,  the  effects  are  magnified 
and  rendered  more  brilliant. 

Measurement  of  the  Waves  of  Light. 

374.  We   are   now  in  a   condition  to  solve   the   im- 
portant problem  of  measuring  the  length  of  a  wave  of 
light. 

375.  The  first  of  our  dark  bands  corresponds,  as  al- 
ready explained,  to  a  difference  of  marginal  path  of  one 
undulation ;  our  second  dark  band  to  a  difference  of  path 
of  two  undulations ;  our  third  dark  band  to  a  difference 
of  three  undulations,  and  so  forth.     With  a  slit  1.35  *  mil- 
limetre wide,  Schwerd  found  the  angular  distance  of  the 
first  dark  band  from  the  centre  of  the  field  to  be  1'  38". 
The  angular  distances  of  the  other  dark  bands  are  twice, 
three  times,  four  times,  etc.,  this  quantity,  that  is  to  say, 
they  are  in  arithmetical  progression. 

376.  Draw  a  diagram  of  the  slit  EC  with  the  beam 

*  The  millimetre  is  about  ^  of  an  inch. 


94  NOTES  ON   LIGHT. 

passing  through  it  at  the  obliquity  corresponding  to  the 
first  dark  band.  Let  fall  a  perpendicular  from  one  edge, 
E,  of  the  slit  on  the  marginal  ray  of  the  other  edge  at  d. 
The  distance,  c  d,  between  the  foot  of  this  perpendicular 
and  the  other  ectge  is  the  length  of  the  wave  of  light. 
From  the  centre  E,  with  the  width  E  c  as  radius,  suppose 
a  semicircle  to  be  described ;  its  radius  being  1.35,  the 
length  of  this  semicircle  is  readily  found  to  be  4.248  milli- 
metres. Now,  the  length  of  this  semicircle  is  to  the  length 
cdof  the  wave  as  180°  to  1'  38",  or  as  648,000*  to  98". 
Thus  we  have  the  proportion — 

648,000  :  98  ::  4.248  to  the  wave-length  cd* 

Making  the  calculation,  we  find  the  wave-length  for  this 
particular  kind  of  light  (red),  to  be  0.000643  of  a  milli- 
metre, or  0.000026  of  an  inch. 

377.  Instead  of  receiving  them  directly  upon  the  retina, 
the  colored  fringes  may  be  received  upon  a  screen.   In  this 
case  it  is  desirable  to  employ  a  lens  of  considerable  con- 
vergent power  to  bring  the  beam  from  the  first  slit  to  a 
focus,  and  to  place  the  second  slit  or  other  diffracting  edge 
or  edges  between  the  focus  and  the  screen.     The  light  in 
this  case  virtually  emanates  from  the  focus. 

378.  If  the  edge  of  a  knife  be  placed  in  the  beam  paral? 
lei  to  the  slit,  the  shadow  of  the  edge  upon  the  screen  will 
be  bounded  by  a  series  of  parallel  colored  fringes.     If  the 
light  be  monochromatic  the  bands  will  be  simply  bright 
and  dark.     The  back  of  the  knife  produces  the  same  effect 
as  its  edge.     A  wooden  or  an  ivory  paper-knife  produces 
precisely  the  same  effect  as  a  steel  knife.     The  fringes  are 
absolutely  independent  of  the  character  of  the  substance 
round  the  edge  of  which  the  light  is  diffracted. 

*  C  d  is  so  minute  that  it  practically  coincides  with  the  circle  drawn 
round  E. 


MEASUREMENT   OF  THE   WAVES   OF   LIGHT.  95 

379.  A   thick   wire   placed   in  the  beam  lias  colored 
fringes  on  each  side  of  its  shadow.     If  the  wire  be  Jine,  or 
if  a  human  hair  be  employed,  the  geometric  shadow  itself 
will  be  found  occupied  by  parallel  stripes.     The  former  are 
called  the  exterior  fringes,  the  latter  the  interior  fringes. 
In  the  hands  of  Young  and  Fresnel  all  these  phenomena 
received  their  explanation  as  effects  of  interference. 

380.  A  slit  consists  of  two  edges  facing  each  other. 
When  a  slit  is  placed  in  the  beam  between  the  focus  and 
the  screen,  the  space  between  the  edges  is  occupied  by 
stripes  of  color. 

381.  Looking  at  a  distant  point  of  light  through  a  small 
circular  aperture  the  point  is  seen  encircled  by  a  series  of 
colored  bands.    If  monochromatic  light  be  used  these  bands 
are  simply  bright  and  dark,  but  with  white  light  the  circles 
display  iris-colors. 

382.  These  results  are  capable  of  endless  variation  by 
varying  the  size,  shape,  and   number  of  the   apertures 
through  which  the  point  of  light  is  observed.     The  street 
lamps  at  night,  looked  at  through  the  meshes  of  a  hand- 
kerchief,  show   diffraction  phenomena.     The   diffraction 
effects  obtained  by  Schwerd  in  looking  through  a  bird's 
feathers  are  very  gorgeous.     The  iridescence  of  Alpine 
clouds  is  also,  an  effect  of  diffraction.* 

*  This  may  be  imitated  by  the  spores  of  Lycopodium.  The  diffrac- 
tion phenomena  of  "  actinic  clouds  "  are  exceedingly  splendid.  One  of 
the  most  interesting  cases  of  diffraction  by  small  particles  that  ever  came 
before  me  was  that  of  an  artist  whose  vision  was  disturbed  by  vividly- 
colored  circles.  When  he  came  to  me  he  was  in  great  dread  of  losing 
his  sight ;  assigning  as  a  cause  of  his  increased  fear  that  the  circles  were 
becoming  larger  and  the  colors  more  vivid.  I  ascribed  the  colors  to 
minute  particles  in  the  humors  of  the  eye,  and  encouraged  him  by  the 
assurance  that  the  increase  of  size  and  vividness  indicated  that  the  dif- 
fracting particles  were  becoming  smaller,  and  that  they  might  finally  be 
altogether  absorbed.  The  prediction  was  verified.  It  is  needless  to  say 


96  NOTES  ON  LIGHT. 

383.  Following  out  the  indications  of  theory,  Poisson 
was  led  to  the  paradoxical  result  that  in  the  case  of  an 
opaque  circular  disk  the  illumination  of  the  centre  of  the 
shadow,  caused  by  diffraction  at  the  edge  of  the  disk,  is 
precisely  the  same  as  if  the  disk  were  altogether  absent. 
This  startling  consequence  of  theory  was  afterward  veri- 
fied experimentally  by  Arago. 

Colors  of  Thin  Plates. 

284.  When  a  beam  of  monochromatic  light — say  of 
pure  red,  which  is  most  easily  obtained  by  absorption — 
falls  upon  a  thin,  transparent  film,  a  portion  of  the  light  is 
reflected  at  the  first  surface  of  the  film ;  a  portion  enters 
the  film,  and  is  in  part  reflected  at  the  second  surface. 

385.  This  second  portion  having  crossed  the  film  to  and 
fro  is  retarded  with  reference  to  the  light  first  reflected. 
The  case  resembles  that  of  our  two  stones"  dropped  into 
still  water  at  unequal  distances  from  the  point  A  (Note 
345). 

386.  If  the  thickness  of  the  film  be  such  .as  to  retard 
the  beam  reflected  from  the  second  surface  a  whole  wave- 
length, or  any  number  of  whole  wave-lengths — or,  in  other 
words,  any  even  number  of  half  wave-lengths — the  two 
reflected  beams,  travelling  through  the  same  ether,  will  be 
in  complete  accordance  /  they  will  therefore  support  each 
other,  and  make  the  film  appear  brighter  than  either  of 
them  would  do  taken  singly. 

387.  But  if  the  thickness  of  the  film  be  such  as  to  retard 
the  beam  reflected  from  the  second  surface  half  a  wave- 
length, or  any  odd  number  of  half- wave  lengths,  the  two 
reflected  beams  will^c  in  complete  discordance  /   and  a 
destruction  of  light  will  follow.     By  the  addition  of  light 

one  word  on  the  necessity  of  optical  knowledge  in  the  case  of  the  prac- 
ticat  oculist. 


COLORS  OF  THIN  PLATES.  97 

which  has  undergone  more  than  one  reflection  at  the  second 
surface  to  the  light  which  has  undergone  only  one  reflec- 
tion, the"  beam  reflected  from  the  first  surface  may  be 
totally  destroyed.  Where  this  total  destruction  of  light 
occurs  the  film  appears  black. 

388.  If  the  film  be  of  variable  thickness,  its  various 
parts  will  appear  bright  or  dark,  according  as  the  thick- 
ness favors  the  accordance  or  discordance  of  the  reflected 
rays. 

389.  Because  of  the  different  lengths  of  the  waves  of 
light,  the  different  colors  of  the  spectrum  require  different 
thicknesses  to  produce  accordance  and  discordance ;  the 
longer  the  waves,  the  greater  must  be  the  thickness  of  the 
film.     Hence  those  thicknesses  which  effect  the  extinction 
of  one  color  will  not  effect  the  extinction   of  another. 
When,  therefore,  a  film  of  variable  thickness  is  illuminated 
by  white  light,  it  displays  a  variety  of  colors. 

390.  These  colors  are  called  the  colors  of  thin  plates. 

391.  The  colors  of  the  soap-bubble;  of  oil  or  tar  upon 
water ;  of  tempered  steel ;  the  brilliant  colors  of  lead  skim- 
mings ;   ISTobili's  metallo-chrome ;   the  flashing  colors  of 
certain  insects'  wings,  are  all  colors  of  thin  plates.     The 
colors  are  produced  by  transparent  films  of  all  kinds.     In 
the  bodies  of  crystals  we  often  see  iridescent  colors  due  to 
vacuous  films  produced  by  internal  fracture.     In  cutting 
the  dark  ice  under  the  moraines  of  glaciers  internal  frac- 
ture often  occurs,  and  the  colors  of  thin  plates  flash  forth 
from  the  body  of  the  ice  with  extraordinary  brilliancy. 

392.  Newton  placed  a  lens  of  small  curvature  in  optical 
contact  with  a  plane  surface  of  glass.     Between  the  lens 
and  the  surface  he  had  a  film  of  air,  which  gradually  aug- 
mented in  thickness  from  the  point  of  contact  outward. 
He  thus   obtained  in  monochromatic  light   a   series  of 
bright  and  dark  rings,  corresponding  to  the  different  thick- 

5 


98  NOTES  ON   LIGHT. 

nesses  of  the  film  of  air,  which  produced  alternate  accord- 
ance and  discordance. 

393.  The  rings  produced  by  violet  he  found  to  be 
smaller  than  those  produced  by  red,  while  the  rings  pro- 
duced by  the  other  colors  fell  between  these  extremes. 
Hence  when  white  light  is  employed,  "  Newton's  Rings  " 
appear  as  a  succession  of  circular  bands  of  color.     A  far 
greater  number  of  the  rings  is  visible  in  monochromatic 
than  in  white  light,  because  the  differently-colored  rings, 
after  a  certain  thickness  of  film  has  been  attained,  become 
superposed  and  reblended  to  form  white  light. 

394.  Newton,  considering  the  means  at  his  disposal, 
measured  the   diameters   of    his   rings  with  marvellous 
accuracy ;   he  also  determined  from  its  focal  length  and  its 
refractive  index  the  diameter  of  the  sphere  of  which  his 
lens  formed  a  part.   He  found  the  squares  of  the  diameters 
of  his  rings  to  be  in  arithmetical  progression,  and  conse- 
quently that  the  thicknesses  of  the  film  of  air  correspond- 
ing to  the  diameters  of  the  rings  were  also  in  arithmetical 
progression. 

395.  He   determined  the   absolute  thicknesses  of  the 
plates  of  air  at  which  the  rings  were  formed.     Employing 
the  most  luminous  rays  of  the  spectrum,  that  is,  the  rays  at 
the  common  boundary  of  the  yellow  and  orange,  he  found 
the  thickness  corresponding  to  the  first  bright  ring  to  be 
__V<nr  of  an  inch. 

396.  The  entire  series  of  bright  rings  were  formed  at 
the  following  successive  thicknesses  : 

TTsWir»  tnftrjnri  TtArhn  inAooj  etc-i 
and  the  series  of  dark  rings,  separating  the  bright  ones,  at 
the  thicknesses 

'1  f  SO'OO)   1180005  TT8 UTTF5   n  8  0  0  0 »  6*C' 

397.  To  account  for  the  rings,  Newton  assumed  that 
the  light  particles  were  endowed  withes  of  easy  transmis- 


COLORS  OF  THIN  PLATES.  99 

sion  and  of  easy  reflection.  He  probably  figured  those 
particles  as  endowed  at  the  same  time  with  a  motion  of 
translation  through  space,  and  a  motion  of  rotation  round 
their  own  axes.  If  we  suppose  such  particles  to  resemble 
little  magnets  which  present  alternately  attractive  and 
repulsive  poles  to  the  surface  which  they  approach,  we 
have  a  conception  in  conformity  wTith  the  notion  of  New- 
ton. 

398.  According  to  this  conception  ordinary  reflection 
and  refraction  would  depend  upon  the  presentation  of  the 
repulsive  or  the  attractive  poles  of  the  particles  to  the 
reflecting  or  refracting  surface. 

399.  Figure  then  the  rotating  light  particles  entering 
the  film  of  air  between  Newton's  lens  and  plate.     If  the 
distance  between  both  be   such  as  to  enable  the  light 
particle  to  perform  a  complete  rotation,  it  will  present  at 
the  second  surface  of  the  film  of  air  the  same  pole  that* it 
presented  at  the  first.     It  will  therefore  be  transmitted, 
and  will  not  return  to  the  eye. 

400.  This  effect  would  also  take  place  if  the  distance 
between  the  plate  and  lens  were  such  as  to  enable  the  light 
particle  to  perform  two,  three,  four,  etc.,  complete  rota- 
tions.    The  dark  rings  of  Newton  were  thus  accounted  for. 
They  occurred  at  places  where  the  light  particles,  instead 
of  being  sent  back  to  the  eye  from  the  second  surface  of 
the  film,  were  transmitted  through  that  surface. 

401.  But  if  the  thickness  of  the  film  be  such  as  to  allow 
the  light  particle  which  has  entered  the  first  surface  to 
perform  only  half  a  rotation  before  it  arrives  at  the  second 
surface ;  then  a  repulsive  pole  will  be  presented  to  the 
latter,  and  the  particle  will  be  driven  back  to  the  eye. 
The  same  will  occur  if  the  distance  be  such  as  to  enable 
the  light  particle  to  perform  three,  or  five,  or  seven,  etc., 
semi-rotations.     The  bright  rings  of  Newton  were  thus 


100  NOTES  ON  LIGHT. 

accounted  for  •  they  occurred  at  places  where  the  light 
particles  on  reaching  the  second  surface  of  the  film  were 
reflected  back  to  the  eye. 

402.  The  theory  of  emission  is  here  at  direct  issue  with 
the  theory  of  undulation.    Newton  assumes  that  the  action 
which  produces  the  alternate  bright  and  dark  rings  takes 
place  at  a  single  surface  ;  i.  e.,  the  second  surface  of  the 
film.     The  undulatory  theory  affirms  that  the  rings  are 
caused  by  the  interference  of  rays  reflected  from  both 
surfaces.     This   has   been  proved  to  be  the   case.     By 
employing  polarized  light  (to  be  subsequently  described 
and  explained)  we  can  destroy  the  reflection  at  the  first 
surface  of  the  film,  and  when  this  is  done  the  rings  vanish 
altogether. 

403.  The  beauty  and  subtlety  of  Newton's  conception 
are,  however,  manifest ;  and  the  theory  was  apparently 
supported  by  the  fact  that  rings  of  feeble  intensity  are 
actually  formed  by  transmitted  light,  and  that  the  bright 
rings  by  transmitted  light  correspond  to  thicknesses  which 
produce  dark  rings  in  reflected  light. 

404.  The  transmitted  rings  are   referred  by  the  un- 
dulatory theory  to  the  interference  of  rays  which  have 
passed  directly  through  the  film,  with  others  which  have 
undergone  two  reflections  within  the  film.     They  are  thus 
completely  accounted  for. 

NOTE. — The  thickness  1^^0o-5-  of  an  inch  referred  to  in 
Note  396,  as  that  corresponding  to  the  first  bright  ring,  is 
one-fourth  of  the  length  of  an  undulation  of  the  light  em- 
ployed by  Newton.  Hence,  in  passing  to  and  fro  through 
the  film,  the  rays  reflected  at  the  second  surface  are  half 
an  undulation  behind  those  reflected  at  the  first  surface. 
At  this  thickness,  therefore,  the  ring  ought,  according  to 
the  principles  of  interference,  to  be  darJc  instead  of  bright. 
The  same  remarks  apply  to  the  thicknesses 


DOUBLE   REFRACTION.  101 

T__5___5  etc. ;  the  former  corresponds  to  a  retardation  of 
three,  and  the  latter  to  a  retardation  of  five  semi-undula- 
tions. With  regard  to  the  dark  rings,  the  first  of  them 
occurs  at  a  thickness  the  double  of  which  is  the  length  of 
a  whole  undulation ;  the  second  of  them  occurs  at  a  thick- 
ness which,  when  doubled,  is  equal  to  two  wave-lengths ; 
the  third  at  a  thickness  the  double  of  which  is  three  wave- 
lengths. Hence,  if  we  take  the  thickness  of  the  film  alone 
into  account,  the  bright  rings  ought  to  be  dark,  and  the 
dark  rings  bright. 

But  something  besides  thickness  is  to  be  considered 
here.  In  the  case  of  the  first  surface  of  the  film  the  wave 
passes  from  the  dense  ethej?-Qf  the  glass  into  the  rare  ether 
of  the  air.  In  the  case  of  the  second  surface  of  the  film 
the  wave  passes  from  the  rare  ether  of  the  air  into  the 
dense  ether  of  the  glass.  This  difference  at  the  two  re- 
flecting surfaces  of  the  film  can  be  proved  to  be  equivalent 
to  the  addition  of  half  a  wave-length  to  the  thickness  of 
the  film.  To  the  absolute  thickness,  therefore,  as  meas- 
ured by  Newton,  half  a  wave-length  is  in  each  case  to  be 
added ;  when  this  is  done  the  rings  follow  each  other  in 
exact  accordance  with  the  law  of  interference  enunciated 
in  Notes  348  to  350. 

Double  Refraction. 

405.  In  air,  water,  and  well-annealed  glass,  the  luminif- 
erous  ether  has  the  same  elasticity  in  all  directions.    There 
is  nothing  in  the  molecular  grouping  of  these  substances 
to  interfere  with  the  perfect  homogeneity  of  tbe  ether. 

406.  But  when  water  crystallizes  to  ice,  the  case  is 
different;    here  the  molecules  are   constrained  by  their 
proper  forces  to  arrange  themselves  in  a  certain  determi- 
nate manner.     They  are,  for  example,  closer  together  in 


102  NOTES  ON  LIGHT. 

some  directions  than  in  others.  This  arrangement  of  the 
molecules  carries  along  with  it  an  arrangement  of  the  sur- 
rounding ether,  which  causes  it  to  possess  different  degrees 
of  elasticity  in  different  directions. 

407.  In  a  plate  of  ice,  for  example,  the  elasticity  of  the 
ether  in  a  direction  perpendicular  to  the  surface  of  freezing 
is  different  from  its  elasticity  in  a  direction  parallel  to  the 
same  surface. 

408.  This  difference  is  displayed  in  a  peculiarly  strik- 
ing manner  by  Iceland  spar,  which  is  crystallized  car- 
bonate of  lime ;  and  in  consequence  of  the  existence  of 
these  two  different  elasticities,  a  wave  of  light  passing 
through  the  spar  is  divided  into  two  ;  the  one  rapid,  cor- 
responding to  the  greater  elasticity,  and  the  other  slow, 
corresponding  to  the  lesser  elasticity* 

409.  Where  the  velocity  is  greatest,  the  refraction  is 
least ;  and  where  the  velocity  is  least  the  refraction  is 
greatest.     Hence  in  Iceland  spar,  as  we  have  two  waves 
moving  with  different  velocities,  we  have  double  refrac- 
tion. 

410.  This  is  also  true  of  the  greater  number  of  crys- 
talline bodies.     If  the  grouping  of  the  molecules  be  not 
in  all  directions  alike,  the  ether  will  not  be  in  all  direc- 
tions equally  elastic,  and  double  refraction  will  infallibly 
result. 

411.  In  rock-salt,  alum,  and  other  crystals,  this  homo- 
geneous grouping  of  the  molecules  actually  occurs,  and 
such  crystals  behave  like  glass,  water,  or  air. 

412.  In  certain  doubly  refracting  crystals  the  molecules 
are  arranged  in  the  same  manner  on  all  sides  of  a  certain 
direction.     For  example,  in  the  case  of  ice  the  molecular 
arrangement  is  the  same  all  round  the  perpendiculars  to 
the  surface  of  freezing. 

413.  In  like  manner,  in  Iceland  spar  the  molecules  are 


DOUBLE   REFRACTION.  103 

arranged  symmetrically  round  the  crystallographic  axis, 
that  is,  round  the  shortest  diagonal  of  the  rhomb  into 
which  the  crystal  may  be  cloven.* 

414.  When  a  beam  of  light  passes  through  ice  per- 
pendicular to  the  surface  of  freezing,  or  through  Iceland 
spar  parallel  to  the   crystallographic   axis,  there  is   no 
double  refraction.     These  cases  are  representative ;  that 
is  to  say,  there  is  no  double  refraction  in  the  direction 
round  which  the  molecular  arrangement  is  in  all  directions 
the  same. 

415.  This  direction  of  no  double  refraction  is  called  the 
optic  axis  of  the  crystal. 

NOTE. — The  vibrations  of  the  ether  being  transverse 
to  the  direction  of  the  ray,  the  elasticity  which  determines 
the  rapidity  of  transmission  is  that  at  right  angles  to  the 
ray's  direction.  In  Iceland  spar  the  velocity  is  slowest 
in  the  direction  of  the  axis  ;  hence  the  elasticity  at  right 
angles  to  the  axis  is  a  minimum.  The  ray,  on  the  other 
hand,  whose  vibrations  are  executed  along  the  axis  is  the 
most  rapid ;  hence  the  elasticity  of  the  ether  along  the 
axis  is  a  maximum.  In  perfectly  homogeneous  bodies 
the  surface  of  elasticity  would  be  spherical ;  it  would  be 
measured  by  the  same  length  of  radius  in  all  directions. 
In  the  case  of  Iceland  spar  the  surface  of  elasticity  is  an 
ellipsoid  whose  longer  axis  coincides  with  the  axis  of  the 
crystal. 

*  The  arrangement  of  the  molecules  is  such,  that  Iceland  spar  may 
be  cloven  with  great  and  equal  facility  in  three  different  directions.  The 
planes  of  cleavage  are  here  oblique  to  each  other.  Rock-salt  also  cleaves 
readily  and  equally  in  three  directions,  the  planes  of  cleavage  being  at 
right  angles  to  each  other.  Hence,  while  rock-salt  cleaves  into  cubes, 
Iceland  spar  cleaves  into  rhombs.  Many  crystals  cleave  with  different 
facilities  in  different  directions.  Selenite  and  crystallized  sugar  (sugar- 
candy)  are  examples. 


104  NOTES  ON  LIGHT. 

Phenomena  presented  by  Iceland  Spar. 

416.  The  two  beams  into  which  the  incident  beam  is 
divided  by  the  spar  do  not  behave  alike.     One  of  them 
obeys  the  ordinary  law  of  refraction ;  its  index  of  refrac- 
tion is  perfectly  constant  and  independent  of  its  direction 
through  the  crystal.     The  angles  of  incidence  and  refrac- 
tion are  in  the  same  plane,  as  in  the  case  of  ordinary  re- 
fraction.    The  ray  which  behaves  thus  is  called  the  ordi- 
nary ray.     In  its  case  the  sine  of  the  angle  of  incidence 
is  to  the  sine  of  the  angle  of  refraction,  or  the  velocity  of 
light  in  air  is  to  its  velocity  in  the  crystal,  in  the  constant 
ratio  of  1.654  to  1..    The  number  1.654  is  the  ordinary 
index  of  Iceland  spar. 

417.  But  the  other  beam  acts  differently.     Its  index 
of  refraction  is  not  constant,  nor  is  the  angle  of  refraction 
as  a  general  rule  in  the  same  plane  as  the  angle  of  inci- 
dence.    The  ray  which  behaves  thus  is  called  the  extraor- 
dinary ray.     If  a  prism  be  formed  of  the  spar  with  its 
refracting   angle   parallel   to   the   optic   axis,   when   the 
incident  beam  traverses  the  prism  at  right  angles  to  the 
optic  axis,  the  separation  of  its  two  parts  is  a  maximum. 
Here  the  full  difference  of  elasticity  between  the  axial 
direction  and  that  perpendicular  to  it  comes  into  play, 
and  the  extraordinary  ray  suffers  its  minimum  retarda- 
tion, and  therefore  its  minimum  refraction.     Its  refractive 
index  is  then  1.483. 

418.  The  index  of  refraction  of  the  extraordinary  ray 
varies  with  its  direction  through  the  crystal  from  1.483  to 
1.654.     The  minimum  value  of  the  ratio  of  the  two  sines, 
or  of  the  two  velocities,  viz.,  1.483,  is  called  the  extraordi- 
nary index. 

419.  When   a   small    aperture    through   which   light 
passes  is  regarded  through  a  rhomb  of  Iceland  spar  two 


PHENOMENA  PRESENTED  BY  ICELAND  SPAR.       105 

apertures  are  seen.  If  the  rhomb  be  placed  over  a  black 
dot  on  a  sheet  of  white  paper,  two  dots  will  be  seen ;  and 
if  the  spar  be  turned,  one  of  the  images  of  the  aperture  or 
of  the  dot  will  rotate  round  the  other. 

420.  The  rotating   image  is  that  formed  by  the  ex- 
traordinary ray. 

421.  One  of  the  two  images  of  the  dot  is  also  nearer 
than  the  other.     The  ordinary  ray  behaves  as  if  it  came 
from  a  more  highly  refractive  medium,  and  the  greater 
the  refraction  the  nearer  must  the  image  appear.     The  ap- 
parent shallowness  of  water  is  referred  to  in  Notes  131 
and   132.     With  bisulphide   of  carbon  the   shallowness 
would  be   more   pronounced,  because   the   refraction  is 
greater.     In  Iceland  spar  the  ordinary  index  bears  nearly 
the  same  relation  to  the  extraordinary  as  the  index  of 
bisulphide  of  carbon  to  that  of  water;  hence  the  ordi- 
nary image  must  appear  nearer  than  the  extraordinary 
one. 

422.  Brewster  showed  that  a  great  number  of  crystals 
possessed  two  optic  axes,  or  two  directions  on  which  a 
beam  passes  through  the  crystal  without  division.     Crys- 
tallized sugar,  mica,  heavy  spar,  sulphate  of  lime,  and  topaz, 
are  examples. 

423.  Thus  crystals  divide  themselves  into — 

I.  Single  refracting  crystals,  such  as  rock-salt,  alum, 
and  fluor-spar ;  and 

II.  Double  refracting  crystals,  of  which  we  have  two 
kinds,  viz.  : 

a.  Uniaxal  crystals,  or  those  with  a  single  optic  axis, 
such  as  Iceland  spar,  rock-crystal,  and  tourmaline ;  and — 

b.  Biaxal  crystals,  or  those  which  possess  two  optic 
axes,  such  as  arragonite,  felspar,  and  those  mentioned  in 
422. 


106  NOTES  ON   LIGHT. 

424.  When  on  a  plate  of  Iceland  spar  cut  perpen- 
dicular to  the  axis,  a  beam  of  light  falls  obliquely,  the 
ordinary  ray  being  the  more  refracted  is  nearer  to  the 
axis  than  the  extraordinary.     The  extraordinary  ray  is  as 
it  were  repelled  by  the  axis.     But  Biot  showed  that  there 
are  many  crystals  in  which  the  reverse  occurs,  in  which,  that 
is  to  say,  the  extraordinary  ray  is  nearer  to  the  axis  than 
the  ordinary,  being  as  it  were  attracted.     The  former  class 
he  called  repulsive  or  negative  crystals ;  Iceland  spar,  ruby, 
sapphire,  emerald,  beryl,  and  tourmaline,  being  examples. 
The  latter  class  he  called  attractive  or  positive  crystals, 
rock-crystal,  ice,  zircon,  being  examples. 

The  Polarization  of  Light. 

425.  The  double  refraction  of  Iceland  spar  was  dis- 
covered by  Erasmus  Bartholinus,  and  was  first  described 
by  him  in  a  work  published  in  Copenhagen  in  1669.     The 
celebrated  Huyghens  sought  to  account  for  the  phenome- 
non on  the  principles  of  a  wave  theory,  and  he  succeeded 
in  doing  so. 

426.  In  his   experiments  on  this   subject,  Huyghens 
found  that  when  a  common  luminous  beam  passes  through 
Iceland  spar  in  any  direction  save  one  (that  of  the  optic 
axis),  it  is  always  divided  into  two  beams  of  equal  intensi- 
ty /  but  that  when  either  of  these  two  half-beams  is  sent 
through  a  second  piece  of  spar,  it  is  usually  divided  into 
two  of  unequal  intensity ;  and  that  there  are  two  posi- 
tions of  the  spar  in  which  one  of  the  beams  vanishes  alto- 
gether. 

427.  On  turning  the  spar  round  this  position  of  absolute 
disappearance,  the  missing  beam  appeared  ;  its  companion 
at  the  same  time  becoming  dimmer ;   both  of  them  then 
passed  through  a  phase  of  equal  intensity,  and  when  the 


THE   POLARIZATION   OF  LIGHT.  107 

rotation  was  continued,  the  beam  which  was  first  trans- 
mitted disappeared. 

428.  Reflecting  on  this  experiment  Newton  came  to 
the  conclusion  that  the  divided  beam  had  acquired  sides 
by  its  passage  through  the  Iceland  spar,  and  that  its  inter- 
ception and  transmission  depended  on  the  way  on  which 
those  sides  presented  themselves  to  the  molecules  of  the 
second  crystal.     He  compared  this  two-sidedness  of  a  beam 
of  light  to  the  two-endedness  of  a  magnet  known  as  its 
polarity ;  and  a  luminous  beam  exhibiting,  this  two-sided- 
ness  was  afterward  said  to  be  polarized. 

429.  In  1808,  Mains,  while   looking  through  a  bire- 
fracting  prism  at  one  of  the  windows  of  the  Luxembourg 
Palace,  from  which  the  solar  light  was  reflected,  found 
that  in  a  certain  position  of  the  spar,  the  ordinary  image 
of  the  window  almost  wholly  disappeared ;   while,  in  a 
position  perpendicular  to  this,  the  extraordinary  image 
disappeared.     He   discerned  the   analogy  between   this 
action  and  that  discovered  by  Huyghensin  Iceland  spar, 
and  came  to  the  conclusion  that  the  effect  was  due  to 
some  new  property  impressed  upon  the  light  by  its  reflec- 
tion from  the  glass. 

430.  What  is  this  property  ?     It  may  be  most  simply 
studied  and  understood  by  means  of  the  crystal  called 
tourmaline.     This   crystal  is   birefractive ;   it   divides   a 
beam  of  light  incident  upon  it  into  two,  but  its  molecular 
grouping,  and  the   consequent   disposition  of  the   ether 
within  it,  are  such  that  one  of  these  beams  is  rapidly 
quenched,  while  the  other  is  transmitted  with  comparative 
freedom. 

431.  It  is  to  be  borne  in  mind  that  the  motions  of  the 
individual  ether  particles  are  transverse  to  the  direction  in 
which  the  light  is   propagated    (read  Note  219).     In  a 


108  NOTES  ON  LIGHT. 

learn  of  ordinary  light  the  mirations  occur  in  all  direc- 
tions round  the  line  of  propagation. 

432.  The  change  suffered  by  light  in  passing  through 
a  plate  of  tourmaline,  of  sufficient  thickness,  and  cut  paral- 
lel to  the  axis  is  this  :   All  vibrations  save  those  executed 
parallel  to  the  axis  are  quenched  within  the  crystal.  Hence 
the  beam  emergent  from  the  plate  of  tourmaline  has  all  its 
vibrations  reduced  to  a  single  plane.     In  this  condition  it 
is  a  beam  of  plane  polarized  l^ahh^ 

433.  Imagine  a  cylindrical  beam  of  light  with  all  its 
ether  particles  vibrating  in  the  same  direction — say  hori- 
zontally— looked  down  upon  vertically,  the  ether  particles, 
if  large  enough,  would  be  seen  performing  their  excursions 
to  and  fro  across  the  direction  of  the  beam.     Looked  at 
crosswise  horizontally,  the  particles  would  be  seen  ad- 
vancing and  retreating,  but  their  paths  would  be  invisible, 
every  ether  particle  covering  its  own  path.     In  the  one 
case  we  should  see  the  lines  of  excursion  ;  in  the  other  case, 
the  ends  of  the   lines   only.     In  this,  according  to  the 
undulatory  theory,  consists  the  two-sidedness  discovered 
by  Huyghens,  and  commented  on  by  Newton. 

Polarization  of  Light  by  ^Reflection. 

434.  The  quality  of  two-sidedness  is  also  impressed 
upon  light  by  reflection.     This  is  the  great  discovery  of 
Malus.     A  beam  reflected  from  glass  is  in  part  polarized 
at  all  oblique  incidences,  a  portion  of  its  vibrations  being 
reduced  to  a  common  plane.     At  one  particular  incidence 
the  beam  is  perfectly  polarized,  all  its  vibrations  being 
reduced  to  the  same  plane.     The  angle  of  incidence  which 
corresponds  to  this  perfect  polarization  is  called  the  polar- 
izing angle. 

435.  The  polarizing  angle  is  connected  with  the  index 


POLARIZATION   OF  LIGHT  BY  REFLECTION.         109 

of  refraction  of  the  medium  by  a  very  beautiful  law  dis- 
covered by  Sir  David  Brewster.*  When  a  luminous  beam 
is  incident  upon  a  transparent  substance,  it  is  in  part 
reflected  and  in  part  refracted.  At  one  particular  inci- 
dence the  reflected  and  refracted  portions  of  the  beam  are 
at  right  angles  to  each  other.  The  angle  of  incidence  is 
then  the  polarizing  angle.  This  is  the  geometrical  expres- 
sion of  the  law  of  Brewster. 

436.  The  polarizing  angle  augments  with  the  refractive 
index  of  the  medium.     For  water  it  is  53°,  for  glass  58°, 
and  for  diamond  68°. 

437.  Thus  a  beam  of  ordinary  light,  whose  vibrations 
are  executed  in  all  directions,  impinging  upon  a  plate  of 
glass  at  the  polarizing  angle,  has,  after  reflection,  all  its 
vibrations  reduced  to  a  common  plane.     The  direction  of 
the  vibrations  of  the  polarized  beam  is  parallel  to  the  polar- 
izing surface. 

438.  Let  a  beam  thus  polarized  by  reflection  at  the 
surface  of  one  plate  of  glass  impinge  upon  a  second  plate 
at  the  polarizing  angle.     In  one  position  of  this  plate  the 
beam  suffers  its  maximum  reflection.     In  a  certain  other 
position  the  beam  is  wholly  transmitted,  there  is  no  reflec- 
tion.    In  this  experiment  the  angle  of  incidence  remains 
unchanged,  nothing  being  altered  save  the  side  of  the  ray 
which  strikes  the  reflecting  surface. 

439.  The  reflection  of  the  polarized  beam  is  a  maxi- 
mum when  the  lines  along  which  the  ether  particles  vibrate 
are  parallel  to  the  reflecting  surface.     It  is  wholly  trans- 
mitted wThen  the  lines  of  vibration  strike  the  reflecting 
surface  at  the  polarizing  angle.     The  reflection  is  then 
zero.     By  taking  advantage  of  this  fact,  the  reflection 
from  the  first  surface  of  a  thin  film  has  been  abolished, 

*  The  index  of  refraction  of  the  medium  is  the  tangent  of  the  polar- 
izing angle. 


110  NOTES  ON  LIGHT. 

Newton's  rings  being  thereby  rendered  incapable  of  for- 
mation, as  stated  in  Note  402. 

440.  A  beam  which  meets  the  first  surface  of  a  plate 
of  glass  with  parallel  sides  at  the  polarizing  angle  meets 
the  second  surface  also  at  its  polarizing  angle,  and  is  in 
part  reflected  there  perfectly  polarized.     Hence,  by  aug- 
menting the  number  of  plates,  the  repeated  reflections  at 
their  limiting  surfaces  furnish  a  polarized  beam  of  greater 
intensity  than  that   obtained   by  reflection  at  a  single 
surface. 

Polarization  of  Light  by  Refraction. 

441.  We  have  hitherto  directed  our  attention  to  the 
reflected  portion  of  the  beam ;  but  the  refracted  portion, 
which  enters  the  glass,  is  also  partially  polarized.     The 
quantities  of  polarized  light  in  the  reflected  and  refracted 
beams  are  always  equal  to  each  other. 

442.  The  plane  of  vibration  in  the  refracted  beam  is  at 
right  angles  to  that  in  the  reflected  beam. 

443.  When  several  plates  of  glass  are  placed  parallel 
to  each  other,  and  a  beam  is  permitted  to  fall  upon  them 
at  the  polarizing  angle,  at  every  passage  from  plate  to 
plate  a  portion  of  the  light  is  reflected  polarized,  an  equal 
portion  of  polarized  light  entering  the  glass  at  the  same 
time.     By  duly  augmenting  the  number  of  plates,  the 
polarization  by  the  successive  refractions  may  be  ren- 
dered sensibly  perfect.     When  this  occurs,  if  any  further 
plates  be  added  to  the  bundle,  reflection  entirely  ceases  at 
their  limiting  surfaces,  the  beam  afterward  being  wholly 
transmitted. 

Polarization  of  Light  by  Double  Refraction. 

444.  In  the  case  last  considered  the  light  was  polarized 
by  ordinary  refraction.    The  polarization  of  light  by  double 


LIGHT   TRANSMITTED  THROUGH  ICELAND   SPAR.    HI 

refraction  has  been  already  touched  upon  in  Notes  432 
and  433.  We  shall  now  extend  our  examination  of  the 
crystal  of  tourmaline  there  referred  to,  and  turn  it  to  ac- 
count in  the  examination  of  other  crystals. 

445.  If  a  beam  of  light  which  has  passed  through  one 
plate  of  tourmaline  impinge  upon  a  second  plate,  it  will 
pass  through  both,  if  the  axes  of  the  two  plates  be  parallel. 
But  if  they  are  perpendicular  to  each  other,  then  the  light 
transmitted  by  the  one  is  quenched  by  the  other,  dark- 
ness marking  the  space  where  the  two  plates  are  super- 
posed. 

446.  If  the  two  axes  be  oblique  to  each  other,  a  portion 
of  the  light  will  pass  through  both  plates.     For,  in  a 
manner  similar  to  the  resolution  of  forces  in  ordinary  me- 
chanics, an  oblique  vibration  may  be  resolved  into  two, 
one  parallel  to  the  axis  of  the  tourmaline,  the  other  per- 
pendicular to  the  axis.     The  latter  component  is  quenched, 
but  the  former  is  transmitted. 

447.  Hence  if  the  axes  of  two  plates  of  tourmaline  be 
perpendicular  to  each  other,  a  third  plate  of  tourmaline 
introduced  obliquely  between  them,  or  a  plate  of  any  other 
crystal  which  acts  in  a  manner  similar  to  the  tourmaline, 
will  transmit  a  portion  of  the  light  emergent  from  the 
first  crystal.     The  plane  of  vibration  of  this  light  being 
oblique  to  the  axis  of  the  second  crystal,  a  portion  of  the 
light  will  also  pass  through  the  latter.     By  the  intro- 
duction, therefore,  of  a  third  crystal,  with  its  axis  oblique, 
we  abolish  in  part  the  darkness  of  the  space  where  the  two 
rectangular  plates  are  superposed. 

Examination  of  Light  transmitted  through  Iceland  Spar. 

448.  We  have  now  to  examine,  by  means  of  a  plate 
of  tourmaline,  the  two  parts  into  which  a  luminous  beam 
is  divided  in  its  passage  through  Iceland  spar. 


NOTES  ON   LIGHT. 

449.  Confining  our  attention  to  one  of  the  two  beams, 
it  is  immediately  found  that  in  a  certain  position  of  the 
plate  the  light  is  freely  transmitted,  while  in  the  per- 
pendicular position  it  is  completely  stopped.     This  proves 
the  beam  emergent  from  the  spar  to  be  polarized. 

450.  From  the  position  of  the  tourmaline  we  can  im- 
mediately infer  the  direction  of  vibration  in  the  polarized 
beam.     If  transmission  occur  when  the  axis  6f  the  plate 
of  tourmaline  is  vertical,  the  vibrations  are  vertical ;  if 
transmission  occur  when  the  tourmaline  is  horizontal,  the 
vibrations  are  horizontal.     The  same  mode  of  investiga- 
tion teaches  us  that  the  second  beam  emergent  from  the 
spar  is  also  polarized. 

451.  The  vibrations  of  the  ether  particles  in  the  two 
beams  are  executed  in  planes  which  are  at  right  angles  to 
each  other.     If  the  vibrations  in  the  one  beam  be  vertical, 
in  the  other  they  are  horizontal.     A  plate  of  tourmaline 
with  its  axis  vertical  transmits  the  former  and  quenches 
the  latter;  while  the  same  plate  held  horizontally,  quenches 
the  former  and  transmits  the  latter. 

452.  A  tourmaline  plate  placed  with  its  axis  vertical, 
in  front  of  the  electric  lamp,  has  its  image  cast  by  a  lens 
upon  a  screen.     A  piece  of  Iceland  spar,  with  one  of  its 
planes   of  vibration  horizontal   and  the   other  vertical, 
placed  in  front  of  the  lens  divides  the  beam  into  two,  and 
yields  two  images  of  the  tourmaline.     One  of  these  images 
is  bright,  the  other  is  dark.     The  reason  is,  that  in  the 
light  emergent  from  the  tourmaline  the  vibrations  are 
vertical,  and  they  can  only  be  transmitted  through  the 
spar  in  company  with  its  vertically  vibrating  beam.,    In 
the  horizontally  vibrating  beam  the  tourmaline  must  ap- 
pear black. 

453.  It  is  also  black  if  the  light  emergent  from  it,  and 
surrounding  it,  meet,  at  the  polarizing  angle,  a  plate  of 


LIGHT   TRANSMITTED  THROUGH  ICELAND  SPAR.    H3 

glass  whose  plane  of  reflection  is  vertical  y  while  it  is 
bright  when  the  light  is  reflected  horizontally.  These 
effects  are  consequences  of  the  law  of  polarization  by  re- 
flection. 

454.  Not    only   do   crystallized    bodies    possess  this 
power  of  double  refraction  and  polarization;  but  all  bodies 
whose  atomic  grouping  is  such  as  to  cause  the  ether  with- 
in them  to  possess  different  elasticities  in  different  direc- 
tions do  the  same. 

455.  Thus  organic  structures  are  usually  double  re- 
fracting.    A  double  refracting  structure  may  also  be  con- 
ferred on   ordinary  glass   by  either  strain  or  pressure. 
Strains  and  pressures  due  to  unequal  heating  also  produce 
double  refraction.     Unannealed  glass  behaves  like  a  crys- 
tal.    A  plate  of  common  window-glass,  which  under  ordi- 
nary circumstances  shows  no  trace  of  double  refraction,  if 
heated  at  a  single  point,  is  rendered  doubly  refractive  by 
the  strains  and  pressures  propagated  round  the  heated 
point.     The  introduction  of  any  of  these  bodies  between 
the  crossed  plates  of  tourmaline  partly  abolishes  the  dark- 
ness caused  by  the  superposition  of  the  plates. 

456.  Two  plates  of  tourmaline,  between  which  bodies 
may  be  introduced  and  examined  by  polarized  light,  con- 
stitute a  simple  form  of  the  polariscope.     The  plate  at 
which  the  light  first  enters  is  called  the  polarizer,  while 
the  second  plate  is  called  the  analyzer. 

457.  But  the  tourmalines  are  small,  usually  colored, 
and  under  no  circumstances  competent  to  furnish  an  in- 
tense beam  of  polarized  light.     If  one  of  the  parts  into 
which  a  prism  of  Iceland  spar  divides  a  beam  of  light 
could  be  abolished,  the  remaining  beam  would  be  polar- 
ized, and,  because  of  the  transparency  of   the  spar,  it 
would  be  far  more  intense  than  any  beam  obtainable  from 
tourmaline. 


114  NOTES  ON   LIGHT. 

458.  This  has  been  accomplished  with  great  skill  by 
Nicol.     He  cut  a  long  parallelopiped  of  spar  into  two  by 
a  very  oblique  section;  polished  the  two  surfaces,  and 
united  them  by  Canada  balsam.     The  refrangibility  of 
the  balsam  lies  between  those  of  the  ordinary  and  the  ex- 
traordinary rays  in  Iceland   spar,  being   less   than  the 
former  and  greater  than  the  latter.     When,  therefore,  a 
beam  of  light  is  sent  along  the  parallelopiped,  the  ordi- 
nary ray,  to  enter  the  balsam,  must  pass  from  a  denser  to 
a  rarer  medium.     In  consequence  of  the  obliquity  of  its 
incidence  it  is  totally  reflected,  and  is  thus  got  rid  of. 
The  extraordinary  ray,  on  the  contrary,  in  passing  from 
the  spar  to  the  balsam  passes  from  a  rarer  to  a  denser 
medium,  and  is  therefore  transmitted.     In  this  way  we 
obtain  a  single  intense  beam  of  polarized  light  (read  Notes 
123,  141,  and  142). 

459.  A  parallelopiped  prepared  in  the  fashion  here  de- 
scribed is  called  a  NicoVs  prism. 

460.  Nicol's  prisms  are  of  immense  use  in  experiments 
on  polarization.     With  them  the  best  polariscopes  are 
constructed.     Reflecting  polariscopes  are  also  constructed, 
consisting  of  two  plates  of  glass,  one  of  which  polarizes 
the  light  by  reflection,  the  other  examining  the  light  so 
polarized.     The  beam  reflected  from  the  polarizer  is  in  this 
case  reflected  or  quenched  by  the  analyzer  according  as 
the  planes  of  reflection  of  the  two  mirrors  are  parallel  or 
at  right  angles  to  each  other. 

Colors  of  Double-refracting  Crystals  in  Polarized  Light. 

461.  A  large  class  of  these  colors  may  be  illustrated 
and  explained  by  reference  to  the  deportment  of  thin 
plates  of  gypsum  (crystallized  sulphate  of  lime,  commonly 
called  selenite)  between  the  polarizer  and  analyzer  of  the 
polariscope. 


COLORS  OF  DOUBLE-REFRACTING  CRYSTALS.        H5 

462.  The  crystal  cleaves  with  'great  freedom  in  one 
direction ;  it  cleaves  with  less  freedom  in  two  others ;  the 
latter  two  cleavages  are  also  unequal.     In  other  words, 
gypsum  possesses  three  planes  of  cleavage,  no  two  of 
which  are  equal  in  value,  but  one  of  which  particularly 
signalizes  itself  by  its  perfection. 

463.  By  following  these  three  cleavages  it  is  easy  to 
obtain  from  the  crystal  diamond-shaped  laminaB  of  any  re- 
quired thinness. 

464..  The  crystal,  as  might  be  expected  from  the  char- 
acter of  its  cleavages,  is  double-refracting.  A  beam  of 
ordinary  light  impinging  at  right  angles  on  a  plate  of 
gypsum,  whose  surfaces  are  those  of  most  perfect  cleavage, 
has .  its  vibrations  reduced  to  two  planes  at  right  angles 
to  each  other ;  that  is  to  say,  the  beam  whose  ether,  prior 
to  entering  the  gypsum,  vibrates  in  all  transverse  direc- 
tions, after  it  has  entered  the  gypsum,  and  after  its 
emergence  from  it,  vibrates  in  two  rectangular  directions 
only. 

465.  The  elasticity  of  the  ether  is  different  in  these 
two  rectangular  directions ;  consequently  the  one  beam 
passes  more  rapidly  through  the  gypsum  than  the  other. 

466.  In  refracting  bodies  generally  the  retardation  of 
the  light  consists  in  a  diminution  of  the  wave-length  of 
the  light.     The  rate  of  vibration  is  unchanged  during 
the  passage  of  the  light  through  the  refracting  body. 
The  case  is  exactly  similar  to  that  of  a  musical  sound 
transmitted  from  water  into  air.     The  velocity  is  reduced 
to  one-fourth  by  the  transfer,  because  the  wave-length  is 
reduced  to  one-fourth.     But  the  pitch,  depending  as  it 
does  on  the  number  of  waves  which  reach  the  ear  in  a 
second,  is  unaltered. 

467.  Because  of  the  difference  of  elasticity  between 
the  two  rectangular  directions  of  vibration  in  gypsum,  the 


116  NOTES  OX  LIGHT. 

waves  of  ether  in  the  one  direction  arc  more  shortened 
than  in  the  other. 

468.  In  the  experiments  with  a  plate  of  gypsnm  now 
to  be  described  and  explained,  we  shall  employ  as  polar- 
izer a  piece  of  Iceland  spar,  one  of  whose  beams  is  in- 
tercepted by  a  diaphragm.     A  Nicol's  prism  shall  be  our 
analyzer. 

469.  When  the  planes  of  vibration  of  the  spar  and 
of  the  Mcol  coincide,  the  light  passes  through  both  and 
may  be  received  upon  a  screen.     When  the  planes  of 
vibration  are  at  right  angles  to  each  other,  the  light  emer- 
gent from  the  spar  is  intercepted  by  the  Nicol,  and  the 
screen  is  dark. 

470.  If  a  plate   of  selenite  be   placed  between   the 
polarizer  and  analyzer,  with  either  of  its  planes  of  vibra- 
tion coincident  with  that  of  the  polarizer  or  analyzer,  it 
produces  no  change  upon  the  screen.     If  the  screen  be 
light,  it  remains  light ;  if  it  be  dark,  it  remains  dark  after 
the  introduction  of  the  gypsum,  which  here  behaves  like 
a  plate  of  ordinary  glass. 

471.  Let  us  assume  the  screen  to  be  dark.     Interpos- 
ing a  thick  plate  of  gypsum  with  its  directions  of  vibra- 
tion oblique  to  that  of  the  polarizer  or  analyzer,  white  light 
reaches  the  screen.     If  the  plate  be  thin,  the  light  which 
reaches  the  screen  is  colored.     If  the  plate  be  of  uniform 
thickness,  the  color  is  uniform.     If  of  different  thicknesses, 
or  if  in  cleaving  thin  scales  cling  to  the  surface  of  the  film, 
some  portions  of  the  plate  will  be  differently  colored  from 
the  rest. 

472.  When  thick  plates  are  employed,  the  different 
colors,  as  in  the  case  of  thin  plates,  are  superposed,  and  re- 
blended  to  white  light. 

473.  The  quantity  of  light  which  reaches  the  eye  is  a 
maximum  when  the  planes  of  vibration  of  the  gypsum 


COLORS  OF  DOUBLE-REFRACTING  CRYSTALS.        H7 

enclose  an  angle  of  45°  with  those  of  the  polarizer  and 
analyzer. 

474.  If  the  plate  of  selenite  be  a  thin  wedge,  and  if  the 
light  be  monochromatic,  say  red,  alternately  bright  (red) 
and  dark  bands  are  thrown  upon  the  screen. 

475.  If,  instead  of  red  light,  blue  be  employed,  the 
blue  bands  are  found  to  occur  at  smaller  thicknesses  than 
those  which  produced  the  red :  other  colors  occur  at  inter- 
mediate thicknesses.    Hence  when  white  light  is  employed, 
instead  of  bands  of  brightness  separated  from  each  other 
by  bands  of  darkness,  we  have  a  series  of  iris-colored 
bands. 

476.  If,  instead  of  a  wedge  gradually  augmenting  in 
thickness  from  the  edge  toward  the  back,  we  employ  a  disk 
gradually  augmenting  in  thickness  from  the  centre  out- 
ward ;  instead  of  a  series  of  parallel  bands  we  obtain  under 
similar  circumstances,  in  white  light,  a  series  of  concentric 
iris-colored  circles. 

477.  Here,  then,  we  have  in  the  first  instance  a  beam 
of  plane  polarized  light  impinging  on  the  selenite.     The 
direction  of  vibration  of  this  beam  is  resolved  into  two 
others  at  right  angles  to  each  other;  namely,  into  the 
two  directions  in  which  the  ether  vibrates  within  the  crys- 
tal.    One  of  these  systems  of  waves  is  retarded  with  refer- 
ence to  the  other. 

478.  But  as  long  as  the  rays  vibrate  at  right  angles  to 
each  other,  they  cannot  interfere  so  as  to  augment  or  di- 
minish the  intensity.     To  effect  such  interference  the  rays 
must  vibrate  in  the  same  place. 

479.  The  function  of  the  analyzer  is  to  reduce  the  two 
rectangular  wave-systems  to  a  single  plane.     Here  the 
effect  of  retardation  is  at  once  felt,  and  the  waves  conspire 
or  oppose  each  other  according  as  their  vibrations  are  in 
the  same  phase  or  in  opposite  phases. 


118    -  NOTES  OX   LIGHT. 

480.  When  the  vibration  planes  of  the  polarizer  and 
analyzer  are  parallel^  a  thickness  of  the  gypsum  crystal 
which  produces  a  retardation  of  half  an  undulation  causes 
the  light  to  be  extinguished  by  the  analyzer. 

481.  When  the  polarizer  and  analyzer  are  crossed,  a 
retardation  of  half  an  undulation,  or  of  any  odd  number 
of  half  undulations,  within  the  crystal  does  not  produce 
extinction  when  these  vibrations  are  compounded  by  the 
analyzer.     A  retardation  of  a  whole  undulation,  or  of  any 
number  of  whole  undulations,  produces  in  this  case  extinc- 
tion.    This,  when  followed  out,  is  a  plain  consequence  of 
the  composition  of  the  vibrations. 

482.  Expressed  generally,  the  phenomena  exhibited  by 
the  parallel  and  crossed  polarizer  and  analyzer  are  com- 
plementary.    If  the  field  be  dark  when  they  are  crossed, 
it  is  bright  when  they  are  parallel.     If  the  field  be  green 
when  they  are  crossed,  it  is  red  when  they  are  parallel ; 
if  yellow  when  they  are  crossed,  it  is  blue  when  they  are 
parallel.     Thus  a  rotation  of  90°  always  brings  out  the 
complementary  color. 

483.  If  instead  of  the  Mcol  we  employ  a  birefracting 
prism  of  Iceland  spar,  the  colors  of  the  selejiite  produced 
by  the  two  oppositely-polarized  beams  will  be  comple- 
mentary.    The  overlapping  of  the  two  colors  always  pro- 
duces   white.      Any   other    double-refracting    substance, 
whether  crystallized,  organized,  mechanically  pressed  or 
strained,  exhibits,  on  examination  by  polarized  light,  phe- 
nomena similar  to  those  of  the  gypsum. 

484.  A  common  beam  of  light  is  equivalent  in  all  its 
effects  to  two  beams  vibrating  in  two  rectangular  planes. 
As  two  such  beams  cannot  interfere,  we  cannot  have  the 
colors  of  the  selenite  in  common  light. 


KINGS  SURROUNDING  THE  AXES  OF  CRYSTALS.        H9 

Rings  surrounding  the  Axes  of  Crystals  in  Polarized 
Light. 

485.  A  pencil  of  rays  passing  along  the  axis  through 
Iceland  spar  suffers  no  division ;  but  if  inclined  to  the  axis, 
however  slightly,  the  pencil  is  divided  into  two,  which 
vibrate  in  rectangular  planes,  and  one  of  which  is  more 
retarded  than  the  other. 

486.  If  the  incident  light  be  polarized,  on  quitting  the 
spar,  oblique  to  the  axis,  it  will  be  in  a  condition  similar 
to  the  light  emergent  from  the  plates  of  gypsum  already 
referred  to.     When  two  rectangular  vibrations,  passing 
through  the  same  ether,  are  reduced  to  the  same  plane  by 
the  analyzer,  interference  occurs  ;  the  two  rays  either  con- 
spiring or  opposing  each  other. 

487.  Whether  they  conspire  or  not  depends  upon  the 
amount  of  relative  retardation,  and  this  again  depends 
upon  the  thickness  of  the  spar  traversed  by  the  two  rays. 
If  they  conspire  at  a  certain  thickness  they  will  also  con- 
spire at  twice  that  thickness,  thrice  that  thickness,  etc. 
Those  thicknesses  at  which  the  rays  conspire  are  separated 
by  others  at  which  they  oppose  each  other. 

488.  With  a  conical  beam  whose  central  ray  passes 
along  the  axis,  the  effects  are  symmetrical  all  round  the 
axis ;  and  when  the  crystal,  illuminated  by  such  a  ray,  is 
examined  by  monochromatic  polarized  light,  we  have  a 
series  of  bright  and  dark  circles  surrounding  the  axis. 

489.  When  the  light  is  red  the  circles  are  larger  than 
when  the  light  is  blue ;  the  smaller  the  wave-length  the 
smaller  are  the  circles.     Hence,  since  the  different  colors 
are  not  superposed,  when  white  light  is  employed  instead 
of  bands  of  alternate  brightness  and  darkness  we  have  ? 
series  of  iris-colored  circles. 


120  NOTES  ON   LIGHT. 

When  the  polarizer  and  analyzer  are  crossed  the  sys- 
tem of  bands  is  intersected  by  a  "black  cross,  whose  arms 
are  parallel  to  the  planes  of  vibration  in  the  polarizer  and 
analyzer.  Those  rays,  whose  planes  of  vibration  within 
the  crystal  coincide  with  the  planes  of  either  the  polarizer 
or  analyzer,  cannot  get  through  either,  and  their  complete 
interception  forms  the  two  arms  of  the  cross.  Those  rays 
whose  planes  of  vibration  enclose  an  angle  of  45°  with 
that  of  the  polarizer  or  analyzer  produce  the  greatest  effect 
when  they  conspire.  At  this  inclination  the  bright  ring 
is  at  its  maximum  brilliancy,  from  which,  right  and  left, 
it  becomes  more  feeble,  until  it  finally  merges  into  the 
darkness  of  the  cross. 

490.  A  rotation  of  90°  produces  here,  as  in  other  cases, 
the  complementary  phenomena :  the  black  cross  becomes 
white,  and  the  circles  change  their  tints  to  complementary 
ones. 

491.  In  crystals  possessing  two  optic  axes  a  series  of 
iris-colored  bands  surround  both  axes,  each  band  forming 
a  curve,  which  its  discoverer,  James  Bernoulli,  called  a 
lemniscata. 

Elliptic  and  Circular  Polarization. 

492.  Two  rays  of  light  vibrating  at  right  angles  to 
each  other,  however  the  one  system  of  vibrations  may  be 
retarded  with  reference  to  the  other,  cannot,  as  already 
stated,  interfere  so  as  to  produce  either  an  increase  or  a 
diminution  of  the  light. 

493.  But  though  the  intensity  remains  unchanged,  the 
rays  act  upon  each  other.     If  one  of  them  differs  from  the 
other  by  any  exact  number  of  semi-undulations,  the  two 
rays  are  compounded  to  a  single  rectilinear  vibration.     In 
all  other  cases  the  resultant  vibration  is  elliptical /  in  one 


ROTARY  POLARIZATION.  121 

particular  case  the  ellipse  in  which  the  individual  particles 
of  ether  move  is  converted  into  a  circle.  This  occurs  when 
one  of  the  systems  of  waves  is  an  exact  quarter  of  an 
undulation  behind  the  other ;  we  have  then  circular  polar- 
ization. 

494.  This  compounding  of  ethereal  vibration  is  me- 
chanically the  same  as  the  compounding  of  the  vibrations 
of  an  ordinary  pendulum ;  or  as  the  compounding  of  the 
vibrations  of  two  rectangular  tuning-forks  by  the  method 
of  Lissajous.* 

495.  Elliptic  polarization  is  the  rule  and  not  the  excep- 
tion.    It  is   particularly  manifested   in  reflection  from 
metals,  and  from  transparent  bodies  which  possess  a  high 
index  of  refraction.  Jamin  has  detected  it  in  light  reflected 
from  all  bodies. 

Rotary  Polarization. 

496.  A  polarized  ray  of  monochromatic  light,  as  al- 
ready stated,  suffers  no  change  during  its  transmission 
through  Iceland  spar  in  the  direction  of  the  optic  axis. 

497.  But  if  transmitted  through  rock-crystal  (quartz) 
in  the  direction  of  the  optic  axis,  its  plane  of  vibration  is 
turned  by  the  crystal.     Supposing  the  polarizer  and  ana- 
lyzer of  the  polariscope  to  be  crossed  so  as  to  produce 
perfect  darkness  before  the  crystal  is  introduced  between 
them,  on  its  introduction  light  will  pass,  and  to  quench 
the  light  the  analyzer  must  be  turned  into  a  new  position. 
The  angle  through  which  the  analyzer  is  turned  measures 
the  rotation  of  the  plane  of  vibration. 

498.  Some  specimens  of  rock-crystal  turn  the  plane  of 
vibration  to  the  right,  and  others  to  the  left.     The  former 
are  called  right-handed  and  the  latter  left-handed  crystals. 

*  See  Lectures  on  Sound,  1st  ed.,  p.  307. 
6 


122  NOTES   ON  LIGHT. 

Sir  John  Herschel  connected  this  optical  difference  with  a 
visible  difference  of  crystalline  form. 

499.  In  the  celebrated  experiment  of  Faraday,  with  a 
bar  of  heavy  glass,  the  plane  of  vibration  was  caused  to 
rotate  both  by  a  magnet  and  an  electric  current ;  the 
direction  of  rotation  bearing  a  constant  relation  to  the 
polarity  of  the  magnet  and  to  the  direction  of  the  current. 

500.  The  subject  of  rotary  polarization  was  examined 
with  great  care  and  completeness  by  Biot,  and  he  estab- 
lished  certain  laws  regarding  it,  two  of  which  may  be 
enunciated  here : 

1.  The  amount  of  the  rotation  is  proportional  to  the 
thickness  of  the  plate  of  rock-crystal. 

2.  The  rotation  of  the  plane  of  vibration  is  different 
for  the  different  rays  of  the  spectrum,  increasing  with  the 
refrangibility  of  the  light. 

Thus  with  a  plate  of  rock-crystal  one  millimetre  thick, 
he  obtained  the  following  rotations  for  the  mean  rays  of 
the  respective  colors  of  the  spectrum  : 


Red,  19°. 
Orange,  21' 
Yellow,  23C 


Green,  28C 
Blue,  32°. 


Indio   36 


Violet,  41 


With  a  plate  two  millimetres  in  thickness  the  rotation  for 
red  is  38°  and  for  violet  82°. 

501.  Since,  then,  the  rays  of  different  colors  emerge 
from  the  rock-crystal  vibrating  in  different  planes,  when 
such  light  falls  upon  the  analyzer  that  color  only  whose 
plane  of  vibration  coincides  with  that  of  the  analyzer  will 
be  transmitted.     By  turning  the  analyzer  we  allow  the 
other  colors  to  pass  in  succession. 

502.  The  phenomena  of  rotary  polarization  are  pro- 
duced by  the  interference  of  two  circularly-polarized  pen- 

of  light,  which  are  propagated  along  the  axis  with 


CONCLUSION.  123 

unequal  velocities,  the  one  revolving  from  left  to  right, 
and  the  other  revolving  in  the  opposite  direction.* 

CONCLUSION. 

I  have  endeavored  in  these  lectures  to  bring  before 
you  the  views  at  present  entertained  by  all  eminent  scien- 
tific thinkers  regarding  the  nature  of  light.  I  have  en- 
deavored to  make  as  clear  to  you  as  possible  that  bold 
theory  according  to  which  space  is  filled  with  an  elastic 
substance  capable  of  transmitting  the  motions  of  light  and 
heat.  And  consider  how  impossible  it  is  to  escape  from 
this  or  some  similar  theory — to  avoid  ascribing  to  light, 
in  space,  a  material  basis.  Solar  light  and  heat  require 
about  eight  minutes  to  travel  from  the  sun  to  the  earth. 
During  this  time  the  light  and  heat  are  .detached  from 
both.  Enclose,  in  idea,  a  portion  of  the  intervening  space 
— say  a  cubic  mile  of  it — occupied  for  a  moment  by  light 
and  heat.  Ask  yourselves  what  they  are.  The  first  in- 
quiry toward  a  solution  is,  What  can  they  do  ?  We  only 
know  things  by  their  effects.  What,  then,  are  the  effects 
which  this  cubic  mile  of  light  and  heat  can  produce  ?  At 
the  earth,  where  we  can  operate  upon  them,  we  find  them 
capable  of  producing  motion.  We  can  lift  weights  with 
them ;  we  can  turn  wheels  with  them ;  we  can  urge  locomo- 
tives with  them ;  we  can  fire  projectiles  with  them.  What 
other  conclusion  can  you  come  to  than  that  the  light  and 
heat  which  thus  produce  motion  are  themselves  motions  f  \ 

One  cubic  mile  of  space,  then,  is  for  a  measurable  time 
the  vehicle  of  motion.  But  is  it  in  the  human  mind  to 
imagine  motion  without  at  the  same  time  imagining  some- 

*  See  Lloyd,  Wave  Theory,  p.  199,  etc. 

f  Sir  William  Thomson  has  attempted  to  calculate  "  the  mechanical 
value  of  a  cubic  mile  of  sunlight." 


124  NOTES  ON  LIGHT. 

thing  moved  ?  Certainly  not.  The  very  conception  of 
motion  necessarily  includes  that  of  a  moving  body.  What, 
then,  is  the  thing  moved  in  the  case  of  our  cubic  mile  of 
sunlight  ?  The  undulatory  theory  replies  that  it  is  a  sub- 
stance of  determinate  mechanical  properties,  a  body  which 
may  or  may  not  be  a  form  of  ordinary  matter,  but  to 
which,  whether  it  is  or  not,  we  give  the  name  of  ether. 
Let  us  tolerate  no  vagueness  here ;  for  the  greatest  dis- 
service that  could  be  done  to  science — the  surest  way  to 
give  error  a  long  lease  of  life — is  to  enshroud  scientific 
theories  in  vagueness.  The  motion  of  the  ether  com- 
municated to  material  substances  throws  them  into  mo- 
tion. It  is,  therefore,  itself  a  material  substance,  for  we 
have  no  knowledge  that  in  nature  any  thing  but  a  material 
substance  can  throw  other  material  substances  into  mo- 
tion. Two  modes  of  motion  are  possible  to  the  ether. 
Either  it  is  shot  through  space  as  a  projectile,  or  it  is  the 
vehicle  of  wave-motion.  The  projectile  theory,  though 
enunciated  by  Newton,  and  supported  by  such  men  as 
Laplace,  Biot,  Brewster,  and  Malus,  has  hopelessly  broken 
down.  Wave-motion,  then,  of  one  kind  or  another,  we 
must  fall  back  upon.  But  how  does  the  Wave  Theory 
account  for  the  phenomena?  Throughout  the  greater 
part  of  these  lectures  we  have  been  answering  this  ques- 
tion. The  cases  brought  before  you  are  representative. 
Thousands  of  facts  might  be  cited  in  illustration  of  each 
of  them,  and  not  one  of  these  facts  is  left  unexplained  by 
the  undulatory  theory.  It  accounts  for  all  the  phenomena 
of  reflection ;  for  all  the  phenomena  of  refraction,  single 
and  double ;  for  all  the  phenomena  of  dispersion ;  for  all 
the  phenomena  of  diffraction ;  for  the  colors  of  thick  plates 
and  thin,  as  well  as  for  the  colors  of  all  natural  bodies.  It 
accounts  for  all  the  phenomena  of  polarization ;  for  all 
those  wonderful  affections,  those  chromatic  splendors  ex- 


CONCLUSION.  125 

hibited  by  crystals  in  polarized  light.  Thousands  of  iso- 
lated facts  might,  as  I  have  said,  be  ranged  under  each 
of  these  heads ;  the  undulatory  theory  accounts  for  them 
all.  It  traces  out  illuminated  paths  through  what  would 
otherwise  be  the  most  hopeless  jungle  of  phenomena  in 
which  human  thought  could  be  involved.  This  is  why 
the  foremost  men  of  the  age  accept  the  ether  not  as  a 
vague  dream,  but  as  a  real  entity — a  substance  endowed 
with  inertia,  and  capable,  in  accordance  with  the  estab- 
lished laws  of  motion,  of  imparting  its  thrill  to  other  sub- 
stances. If  there  is  one  conception  more  firmly  fixed  in 
modern  scientific  thought  than  another,  it  is  that  heat  is 
a  mode  of  motion.  Ask  yourselves  how  the  vast  amount 
of  mechanical  energy  actually  transmitted  in  the  form 
of  heat  reaches  the  earth  from  the  sun.  Matter  must  be 
its  vehicle,  and  the  matter  is  according  to  theory  the 
luminiferous  ether. 

Thomas  Young  never  saw  with  his  eyes  the  waves  of 
sound;  but  he  had  the  force  of  imagination  to  picture 
them  and  the  intellect  to  investigate  them.  And  he  rose 
from  the  investigation  of  the  unseen  waves  of  air  to  that 
of  the  unseen  waves  of  ether ;  his  belief  in  the  one  being 
little,  if  at  all,  inferior  to  his  belief  in  the  other.  One  ex- 
pression of  his  will  illustrate  the  perfect  definiteness  of 
his  ideas.  To  account  for  the  aberration  of  light  he 
thought  it  necessary  to  assume  that  the  ether  which  en- 
compasses the  earth  does  not  partake  of  the  motion  of  our 
planet  through  space.  His  words  are :  "  The  ether  passes 
through  the  solid  mass  of  the  earth  as  the  wind  passes 
through  a  grove  of  trees."  This  bold  assumption  has 
been  shown  to  be  unnecessary  by  Prof.  Stokes,  who  proves 
that,  by  ascribing  to  the  ether  properties  analogous  to 
those  of  an  elastic  solid,  aberration  would  be  accounted 


126  NOTES  ON  LIGHT. 

for,  without  supposing  the  earth  to  be  thus  permeable. 
Stokes  believes  in  the  ether  as  firmly  as  Young  did. 

I  may  add,  that  one  of  the  most  refined  experimenters 
in  France,  M.  Fizeau,  who  is  also  a  a  member  of  the  Insti- 
tute, undertook  to  determine,  some  years  ago,  whether  a 
moving  body  drags  the  ether  along  with  it  in  its  motion. 
His  conclusion  is,  that  part  of  the  ether  adheres  to  the 
molecules  of  the  body,  and  is  transferred  along  with 
them.  This  conclusion  may  or  may  not  be  correct ;  but 
the  mere  fact  that  such  experiments  were  undertaken  by 
such  a  man  illustrates  the  distinctness  with  which  this 
idea  of  an  ether  is  held  by  the  most  eminent  scientific 
workers  of  the  age. 

But  while  I  have  endeavored  to  place  before  you  with 
the  utmost  possible  clearness  the  basis  of  the  undulatory 
theory,  do  I  therefore  wish  to  close  your  eyes  against  any 
evidence  that  may  arise  of  its  incorrectness  ?  Far  from 
it.  You  may  say,  and  justly  say,  that  a  hundred  years 
ago  another  theory  was  held  by  the  most  eminent  men, 
and  that,  as  the  theory  then  held  had  to  yield,  the  undu- 
latory theory  may  have  to  yield  also.  This  is  perfectly 
logical.  Just  in  the  same  way,  a  person  in  the  time  of 
Newton,  or  even  in  our  own  time,  might  reason  thus :  The 
great  Ptolemy,  and  numbers  of  great  men  after  him,  be- 
lieved that  the  earth  was  the  centre  of  the  solar  system. 
Ptolemy's  theory  had  to  give  way,  and  the  theory  of 
gravitation  may,  in  its  turn,  have  to  give  way  also.  This 
is  just  as  logical  as  the  former  argument.  The  strength 
of  the  theory  of  gravitation  rests  on  its  competence  to  ac- 
count for  all  the  phenomena  of  the  solar  system ;  and  how 
strong  that  theory  is  will  be  understood  by  those  who 
have  heard  in  this  room  Prof.  Grant's  lucid  account  of  all 


CONCLUSION.  127 

that  it  explains.  On  a  precisely  similar  basis  rests  the 
undulatory  theory  of  light ;  only  that  the  phenomena  which 
it  explains  are  far  more  varied  and  complex  than  the  phe- 
nomena of  gravitation.  You  regard,  and  justly  so,  the 
discovery  of  Neptune  as  a  triumph  of  theory.  Guided  by 
it,  Adams  and  Leverrier  calculated  the  position  of  a  plane- 
tary mass  competent  to  produce  the  disturbances  of  Uranus. 
Leverrier  communicated  the  result  of  his  calculation  to 
Galle,  of  Berlin ;  and  that  same  night  Galle  pointed  the 
telescope  of  the  Berlin  Observatory  to  the  portion  of  the 
heavens  indicated  by  Leverrier,  and  found  there  a  planet 
36,000  miles  in  diameter. 

It  so  happens  that  the  undulatory  theory  has  also  its 
Neptune.  Fresnel  had  determined  the  mathematical  ex- 
pression for  the  wave-surface  in  crystals  possessing  two 
optic  axes ;  but  he  did  not  appear  to  have  an  idea  of  any 
refraction  in  such  crystals  other  than  double  refraction. 
While  the  subject  was  in  this  condition  the  late  Sir  Wil- 
liam Hamilton,  of  Dublin,  a  profound  mathematician, 
took  it  up,  and  proved  the  theory  to  lead  to  the  conclu- 
sion that  at  four  special  points  of  the  wave-surface  the 
ray  was  divided  not  in  two  parts,  but  into  an  infinite 
number  of  parts ;  forming  at  those  points  a  continuous 
conical  envelope  instead  of  two  images.  No  human  eye 
had  ever  seen  this  envelope  when  Sir  William  Hamilton 
inferred  its  existence.  If  the  theory  of  gravitation  be 
true,  said  Leverrier,  in  effect,  to  Dr.  Galle,  a  planet  ought 
to  be  there :  if  the  theory  of  undulation  be  true,  said  Sir 
William  Hamilton  to  Dr.  Lloyd,  my  luminous  envelope 
ought  to  be  there.  Lloyd  took  a  crystal  of  Arragonite, 
and  following  with  the  most  scrupulous  exactness  the  in- 
dications of  theory,  discovered  the  envelope  which  had 
previously  been  an  idea  in  the  mind  of  the  mathematician. 


128  NOTES  ON  LIGHT. 

Whatever  may  be  the  strength  which  the  theory  of  gravi- 
tation derives  from  the  discovery  of  Neptune,  it  is  matched 
by  the  strength  which  the  undulatory  theory  derives  from 
the  discovery  of  conical  refraction. 


NOTE. 

I  would  strongly  recommend  for  perusal  the  essay  on 
Light,  published  in  Sir  John  Herschel's  "  Familiar  Lectures 
on  Scientific  Subjects." 

J.  T. 


NOTES 

OF    A    COURSE    OF    SEVEN    LECTURES    ON 

ELECTRICITY. 


NOTES    ON    EL-EGTEIOITT. 


Voltaic  ^Electricity :  the  Voltaic  Battery. 

1.  IF  two  pieces  of  the  same  metal  (pure  zinc  or  pure 
platinum,  for  example)  be  immersed  in  water,  which  has 
been  rendered  sour  by  the  addition  of  a  little  sulphuric 
acid,  the  acidulated  water  attacks  neither. 

The  ordinary  zinc  of  commerce  being  rendered  impure 
by  the  admixture  of  other  metals  is  attacked  by  the  acid. 
It  may,  however,  be  enabled  to  withstand  the  acid  by 
covering  its  surface  with  mercury.  The  zinc  is  dissolved 
by  the  mercury,  detached  from  its  impurities,  and  pre- 
sented to  the  liquid.  This  process  is  called  amalga- 
mation. 

2.  If  two  pieces  of  two  different  metals  (pure  zinc  and 
platinum,  for  example)  be  immersed  in  acidulated  water, 
no  sensible  action  occurs  as  long  as  the  metals  do  not  touch 
each  other  •  but  the  moment  they  touch,  and  as  long  as 
they  continue  in  contact,  the  zinc  is  attacked  by  the  acid- 
ulated water  and   dissolves,  while  bubbles  of  gas  rise 
from  the  surface  of  the  platinum. 

3.  This  gas  when  collected  proves  to  have  the  specific 
gravity  of  hydrogen ;  like  hydrogen  it  also  burns  in  the 
air.     The  water,  in  fact,  is  decomposed  by  the  touching 
metals ;  its  oxygen  unites  with  the  zinc  to  form  oxide  of 
zinc,  while  its  hydrogen  escapes  from  the  platinum. 


132  NOTES  ON   ELECTRICITY. 

4.  If  the  two  metals  be  only  partially  plunged  into  the 
acidulated  water,  it  does  not  matter  whether  contact  oc- 
curs within  the  liquid  or  outside  of  it.     The  effect  in  both 
cases  is  the  decomposition  of  the  water,  the  solution  of 
the  zinc,  and  the  liberation  of  the  hydrogen  gas. 

5.  When  the  two  partially  immersed  metals  arc  con- 
nected outside  the  liquid  by  a  long  wire  (say  of  copper) 
the  effect  is  the  same  as  when  they  touch  directly.     In 
both  cases  a  circuit  is  said  to  be  formed,  consisting  of  the 
two  metals  and  the  liquid.     In  the  case  last  mentioned 
the  copper  wire  is  said  to  complete  the  circuit. 

For  these  experiments  a  strip  of  platinum  and  a  strip 
of  amalgamated  zinc  are  employed.  The  liquid  is  placed 
in  a  glass  cell  with  parallel  sides,  through  which  is  sent  a 
beam  of  light,  and  by  means  of  a  lens  a  magnified  image 
of  the  cell  and  its  two  strips  is  cast  upon  a  screen.  The 
chemical  action  consequent  upon  touching  the  metals, 
or  on  completing  the  circuit  with  a  wire,  and  its  suspension 
when  contact  is  interrupted,  are  then  very  plainly  seen. 

6.  The  wire  is  also  said  to  be  the  vehicle  of  an  electric 
current  which  flows  round  the  circuit.     It  is  also  called  a 
Voltaic  current,  because  the  action  here  described  was 
discovered  by  the  celebrated  Italian  philosopher  Yolta. 
These  terms,  however,  convey  to  ug,  as  yet,  no  meaning. 
Our  sole  business  during  the  present  lecture  is  to  examine 
the  wire  which  completes  the  circuit,  and  to  determine 
wherein  it  differs  from  an  ordinary  wire. 

7.  And  to  enable  ourselves  to  do  this  effectually,  we 
shall  employ  an  arrangement,  or  a  combination,  of  zinc 
and  platinum  plates  and  acids,  known  as  a  voltaic  battery. 
We   shall   subsequently   analyze    this    battery,   and   de- 
termine what  occurs  within  it.     For  the  present,  as  afore- 
said, we  shall  confine  ourselves  to  the  examination  of  the 
wire  which  completes  the  circuit  outside  the  battery. 


ELECTRO-MAGNETISM:  ELEMENTARY  PHENOMENA.    133 

Electro-Magnetism :  Elementary  Phenomena. 

8.  Interrupting  the  circuit,  and  immersing  the  wire  in 
iron  filings,  it  shows  no  power  of  attraction  over  them. 
Establishing  the  circuit,  on  reimmersing  the  wire  in  the 
filings  they  cluster  round  it  and  cling  to  it.     If  the  wire 
be  raised  out  of  the  filings,  they  form  an  envelope  round 
it.     The  moment,  however,  the  circuit  is  interrupted,  the 
filings  fall. 

9.  If  the  wire  be  disconnected  from  the  plates  of  plat- 
inum and  zinc,  and  stretched  under  and  parallel  to  a  sus- 
pended bar  magnet,  no  action  is  observed ;  but  on  mak- 
ing the  wire,  stretched  beneath  the  magnet,  form  part  of 
a  voltaic  circuit,  the  magnet  is  deflected  from  the  mag- 
netic meridian.     This  is  OErsted's  discovery. 

10.  To  the  eye  the  wire,  if   tolerably  thick,  is  un- 
changed by  its  connection  with  the  zinc  and  platinum. 
But  if  for  the  thick  copper  wire  a  thin  platinum  wire  be 
substituted  it  is  sensibly  heated,  and  may  even  be  caused 
to  glow  brightly.     The  wire  therefore  must  be  the  vehicle 
of  some  power  or  condition,  which  is  competent  to  pro- 
duce both  magnetic  and  thermal  phenomena. 

11.  If  a  naked  wire,  forming  part  of  a  voltaic  circuit,  be 
wound  round  a  bar  of  iron,  the  power  of  which  the  wire 
was  the  vehicle  is  in  great  part  transmitted  to  the  iron 
which  becomes  part  of  the  circuit. 

12.  But  if  the  wire  be  overspun  with  cotton,  or  still 
better  with  silk,  this  transmission  of  the  power  from  the 
wire  to  the  iron  bar  is  prevented.     The  wire  may  then  be 
coiled  round  the  bar  while  the  power  is  compelled  to  pass 
in  succession  through  all  the  convolutions  of  the  wire. 
Here  the  iron  bar  is  not  at  all  in  the  circuit. 

13.  But  though  not  in  the  circuit  it  is  powerfully  ex- 
cited by  the  surrounding  wire.     Every  convolution  of  the 


134  NOTES  ON   ELECTRICITY. 

wire  evokes  a  certain  amount  of  magnetism  in  the  bar ; 
and  by  rendering  the  convolutions  sufficiently  numerous, 
a  magnet  of  enormous  strength  may  be  thus  generated. 
This  is  Sturgeon's  application  of  Arago's  discovery. 

14.  Such  a  magnet  is  called  an  Electro-magnet  to  dis- 
tinguish it  from  ordinary  permanent  steel  magnets.    When 
the   circuit  is  broken  the  power  of  the  electro-magnet 
ceases.     It  then  falls  from  its  highly-excited  condition  to 
the  condition  of  ordinary  iron. 

15.  For  electro-magnetic  purposes  the  covered  wire  is 
usually  coiled  round  a  hollow  reel,  several  layers  of  coil 
being  sometimes  superposed  upon  each  other.     In  this 
condition  the  reel  is  called  an  electro-magnetic  helix.     The 
iron  bar  to  be  magnetized  is  placed  within  the  helix,  form- 
ing its  core.     The  electro-magnet  may  be  either  straight, 
shaped  like  a  horseshoe,  or  it  may  be  caused  to  assume 
other  forms. 

16.  The  smooth  bar  of  iron  placed  across  the  ends,  or 
poles,  of  a  horseshoe  magnet,  is  sometimes  called  a  keeper, 
sometimes  an  armature,  and  sometimes  a  sub-magnet. 

17.  It  is  not  necessary  that  the  convolutions  of  the 
helix  should  be  close  to  the  core.     A  hoop,  for  example, 
a  yard  in  diameter,  round  which  covered  wire  is  coiled, 
magnetizes  an  iron  bar  placed  across  it  at  its  centre.     The 
magnetized  body  is  here  nearly  18  inches  from  the  mag- 
netizing coil.     How  is  the  power  transmitted  from  the  one 
to  the  other  ?    Is  it  an  action  at  a  distance,  or  does  it  re- 
quire a  medium  for  its  propagation  ?     I  do  not  know. 
The  question  at  present  profoundly  interests  investiga- 
tors. 

18.  If  a  covered  wire  forming  part  of  a  voltaic  circuit 
be  coiled  round  an  iron  bar  near  one  of  its  ends,  there  is  a 
propagation  of  the  excitement  along  the  bar  toward  the 
distant  end.     As  the  coils  augment  in  number  the  attrac- 


ELECTRO-MAGNETIC  ENGINES.  135 

tive  power  of  the  distant  end  increases.  On  undoing  the 
coils  the  magnetism  gradually  falls.  The  process  resem- 
bles more  or  less  the  conduction  of  heat.  The  augmenta- 
tion of  the  coils  answering  to  the  increasing  of  the  tem- 
perature, and  the  undoing  of  the  coils  answering  to  the 
cooling  of  the  end  of  the  bar. 

Electro-Magnetic  Engines. 

19.  When  the  end -of  a  cylinder  of  iron  is  partially  in- 
troduced into  an  electro-magnetic  helix,  on  completing  the 
circuit  a  force  of  suction  is  exerted  upon  it  tending  to  draw 
it  into  the  helix.     Page  turned  this  force  to  account  in  the 
construction  of  an  electro-magnetic  engine. 

Hollow  iron  cylinders,  which  pass  freely  into  the 
helix,  are  employed  for  this  experiment.  The  end  only 
of  the  hollow  cylinder  being  introduced,  when  the  circuit 
is  completed  the  cylinder  is  suddenly  and  strongly 
sucked  in. 

20.  Others  have  turned  to  account  mechanically  the 
attraction  exerted  by  electro-magnetic  cores  on  bars  of 
iron.    The  distinguished  electro-mechanician  Froment  pro- 
duced rotatory  motion  in  this  way.     A  series  of  electro- 
magnets are  so  ranged  that  their  poles  lie  facing  each 
other  along  the  circumference  of  a  circle ;  and  a  series  of 
transverse  bars  of  iron  are  so  connected  together  as  to  be 
able  to  approach  the  poles  in  succession,  and  rotate  as  a 
system.     "When  the  circuit  is  established,  these  bars  are 
attracted,  motion  being  thus  imparted  to  the  system.    The 
bars  on  arriving  at  the  poles  which  attract  them  suddenly 
cease  to  be  attracted ;  the  magnetism  being  temporarily 
suspended  to  allow  each  bar  to  pass  forward,  with  the 
velocity  impressed  upon  it,  to  the  next  pair  of  attracting 
poles.     On  reaching  these  the  magnetism  is  again  tem- 
porarily  suspended.      Thus   the   bars   are  never  pulled 


136  NOTES  ON    ELECTRICITY. 

back  /  and  in  this  way  a  continuous  motion  of  rotation  is 
maintained. 

21.  This  rotatory  motion  can  be  applied  in  various 
ways ;  it  may,  for  example,  be  caused  to  pump  water,  to 
saw  wood,  or  to  drive  piles. 

One  of  Froment's  electro-magnetic  engines,  and  its 
application  to  pumping  and  pile-driving,  is  employed  to 
illustrate  this. 

Physical  Effects  of  Magnetization. 

22.  Sound  is  one  of  the  physical  effects  which  accom- 
pany sudden  magnetization  and  sudden  demagnetization. 
An  ear  placed  close  to  an  iron  core  hears  a  clink  the  mo- 
ment the  circuit  is  established  round  it.     A  clink  is  also 
heard  when  the  circuit  is  broken.  This  is  Page's  discovery. 
Employing  a  contact-breaker  (in  a  distant  room  to  abolish 
its  noise)  the  coil  may  be  magnetized  and  demagnetized 
in  quick  succession ;  the  sounds  then  produced  may  be 
heard  by  several  hundreds  at  once. 

A  poker  of  good  soft  iron  placed  within  an  electro- 
magnetic helix,  and  with  its  two  ends  supported  on  wooden 
trays,  produces  a  very  good  effect.  The  sound  may  be 
rendered  musical. 

23.  When  an  iron  bar  is  magnetized  its  volume  is  un- 
changed, but  its  shape  is  altered.     It  lengthens  in  the 
direction  of  magnetization.     This  is  Joule's  discovery. 

24.  Joule  employed  a  system  of  levers  to  augment  the 
effect,  and  a  microscope  to  observe  the  elongation  thus 
augmented.    Our  method  is  this :  The  iron  bar  is  magnet- 
ized by  an   electro-magnetic  helix  which   surrounds  it. 
Its  elongation  is  first  augmented  fiftyfold  by  means  of  a 
lever;  and  this  motion  is  applied  to  turn  the  axis  of  a 
rotating  mirror.    From  the  mirror  is  reflected  a  long  beam 
of  light,  which  forms  an  index  without  weight.     The  re- 


PHYSICAL  EFFECTS  OF  MAGNETIZATION.  137 

fleeted  beam  may  be  caused  to  print  a  circle  of  light  upon 
a  white  screen,  and  this  circle  when  the  bar  is  magnetized, 
suffers  a  displacement  due  to  the  elongation  of  the  bar. 
This  displacement  may  amount  to  a  foot  or  more. 

What  is  the  cause  of  this  elongation  ?  The  discussion 
of  this  question  requires  some  preliminary  knowledge. 

25.  If  a  sheet  of  paper  or  a  square  of  glass  be  placed 
over  a  magnet,  iron  filings  scattered  on  the  paper  or  on 
the  glass  arrange  themselves  in  lines,  which  Faraday  called 
Lines  of  Force.     Along  these  lines  the  filings  set  their 
longest  dimensions,  and  they  also  attach  themselves  end 
to  end.     A  little  bar  of  iron,  or  a  small  magnetic  needle, 
freely  suspended,  sets   itself  also   along  these   lines  of 
force. 

The  formation  and  modifications  of  the  magnetic  curves, 
or  lines  of  force,  are  shown  in  this  lecture  by  means  of  small 
magnets  held  between  plates  of  glass  and  strongly  illumi- 
nated. Magnified  images  of  the  curves  are  thrown  upon 
a  screen  about  40  feet  distant.  The  shifting  of  the  curves 
by  the  tapping  of  the  glass  is  plainly  visible. 

26.  We  may  regard  a  bar  of  iron  as  made  up  of  parti- 
cles united  by  the  force  of  cohesion,  but  still  to  some  ex- 
tent distinct.     When  iron  is  broken  we  see  crystalline 
facets  on  the  surface  of  fracture.     In  fact,  the  bar  is  com- 
posed of  minute  crystals  of  irregular  shape.     These,  when 
the  bar  is  magnetized,  try  to  set  their  longest  dimensions 
parallel  to  the  direction  of  magnetization,  that  is  to  say, 
in  the  direction  of  the  bar  itself.     They  succeed  in  this 
effort  to  some  slight  extent,  and  thus  produce  the  minute 
and  temporary  lengthening  of  the  bar.     This  is  the  ex- 
planation of  De  la  Rive.     It  is,  I  think,  as  true  as  it  is 
acute. 

27.  Magnetic  oxide  of  iron  may  be  suspended  as  a 
powder  in  water  contained  in  a  cylindrical  vessel  with  flat 


138  NOTES  ON  ELECTRICITY. 

glass  ends.  Let  the  vessel  be  surrounded  by  a  coil  of 
covered  wire.  Looking  at  a  candle  through  the  muddy 
liquid,  and  making  the  coil  part  of  a  voltaic  circuit,  the 
candle  brightens  at  the  moment  the  circuit  is  made. 
Breaking  the  circuit,  dimness  again  supervenes.  This  is 
due  to  an  arrangement  of  the  particles  of  suspended  oxide 
similar  to  that  of  the  iron  filings.  They  set  their  longest 
dimensions  parallel  to  the  beam  of  light,  and  thus  obstruct 
its  passage  less.  They  also  attach  themselves  end  to  end, 
and  form  lines  like  the  lines  of  filings.  This  beautiful  ex- 
periment is  due  to  Grove. 

Projecting  a  magnified  image  of  the  end  of  the  cylin- 
drical cell  on  a  screen,  and  sending  through  it  the  beam 
of  the  electric  lamp  whenever  the  circuit  is  established, 
an  illuminated  disk,  2  or  3  feet  in  diameter,  flashes  out 
upon  the  screen. 

Character  of  Magnetic  Force. 

It  is  necessary  to  our  further  progress  to  have  clear 
and  definite  ideas  as  to  the  character  of  the  magnetic 
force. 

28.  The  magnetic  power  of  a  magnet,  or  of  a  mag- 
netic needle,  though   really  distributed   throughout  its 
mass,  appears  to  be  concentrated  at  two  points  near  the 
ends.     These  points  are  called  the  poles  of  the  magnet  or 
needle. 

29.  The  magnetic  power  of  the  earth  is  doubtless  also 
distributed  through  the  mass  of  the  earth,  but  a  concen- 
tration similar  to  that  just  noticed  endows  the  earth  also 
with  magnetic  poles. 

30.  The  action  of  the  earth  upon  a  magnetic  needle  is 
this:    the  north  terrestrial  pole  repels   one  end  of   the 
needle  and  attracts  the  other ;  the  south  magnetic  pole 
also  attracts  one  end  of  the  needle  and  repels  the  other. 


CHARACTER  OF  MAGNETIC  FORCE.  139 

But  the  end  attracted  by  the  north  terrestrial  pole  is  re- 
pelled by  the  south,  while  the  end  attracted  by  the  south 
is  repelled  by  the  north. 

31.  Thus  to  each  terrestrial  magnetic  pole  the  needle 
presents  two  ends  which  are  differently  endowed.     Two 
opposite  kinds  of  magnetism  may  be  supposed  to  be  con- 
centrated at  the  two  ends.     In  this  douUeness  of  the  mag- 
netic force  consists  what  is  called  magnetic  polarity. 

32.  Each  of  the  two  distinct 'kinds  of  magnetism  may 
be  regarded  as  self-repellent.     North  repels  north,  and 
south  repels  south.     But  different  kinds  of  magnetism  are 
mutually  attractive ;  south  attracts  north,  and  north  at- 
tracts south. 

33.  When  a  magnet,  or  a  magnetic  needle,  is  suspended 
with  the  line  joining  its  poles  oblique  to  the  magnetic 
meridian,  the  earth's  action  on  the  needle  resolves  itself 
into  what  in  mechanics  is  called  "  a  couple,"  tending  to 
turn  the  needle  into  the  magnetic  meridian. 

34.  When  the  needle  is  in  the  meridian,  the  two  forces 
which  constitute  the  couple  are  opposite  and  equal.     The 
tendency  to  produce  rotation  then  ceases ;  the  needle  is 
in  its  position  of  equilibrium. 

35.  When  the  forces  are  equal  and  opposite  they  must 
neutralize  each  other ;  no  motion  of  translation  of  the 
needle  being,  therefore,  possible.     Thus,  when  the  needle 
is  caused  to  swim  on  water,  or  on  mercury,  it  does  not 
move  toward  either  of  the  terrestrial  magnetic  poles. 

36.  One  pole  of  a  bar  magnet  repels  the  one  end  and 
attracts  the  other  end  of  a  magnetic  needle.     At  the  other 
pole   of  the   magnet   the   attraction   and   repulsion   are 
reversed.     In  the  middle  of  the  magnet  is  the  magnetic 
equator,  where  neither  end  of  the  needle  is  attracted  or 
repelled. 


140  NOTES  ON  ELECTRICITY. 

Magnetism  of  Helix :  Strength  of  Electro-Magnets. 

3V.  An  electro-magnetic  helix,  even  without  a  core  of 
iron,  behaves  exactly  like  a  magnet.  It  attracts  iron. 
Its  two  ends,  moreover,  are  opposite  poles,  and  between 
them  is  a  magnetic  equator.  When,  however,  a  core  is 
placed  within  the  helix,  the  magnetism  of  the  combined 
system  is  far  more  intense  than  that  of  the  helix  alone. 

38.  The  strength  of  a"  magnet  is  measured  by  its  power 
to  deflect  a  magnetic  needle  from  its  meridian ;  the  mag- 
netic strength  of  a  helix  alone,  and  of  a  helix  and  core 
combined,  are  similarly  determined. 

39.  To  obtain  the  magnetic  strength  of  the  core  alone, 
we  first  determine  the  strength  of  the  helix  alone,  then 
that  of  the  helix  and   core  combined;    subtracting  the 
former  strength  from  the  latter,  we  obtain  the  magnetic 
strength  of  the  core. 

40.  If  the  cores  be  thick  and  formed  of  good  iron,  the 
magnetic  strength  of  the  core  is  exactly  proportional  to 
that  of  the  helix.     A  helix  of  double  power  will  produce 
an  electro-magnet  of  double  strength ;  a  helix  of  treble 
power,  an  electro-magnet  of  treble  strength,  and  so  on. 
Thus  by  varying  the  strength  of  the  helix  we  vary  in  like 
degree  the  strength  of  the  iron  core  within  it. 

Electro-Magnetic  Attractions :  Law  of  Squares. 

41.  And  here  an  important  point  arises.     When  we 
allow  a  core  of  double  power  to  act  upon  a  piece  of  good 
iron,  nearly  but  not  quite  in  contact  with  the  core,  the 
attraction  of  the  iron  is  not  doubled,  but  quadrupled.     If 
the  core  be  of  treble  power,  the  attraction  is  not  only 
trebled,   but    it    increases    ninefold.      If   the    magnetic 
strength  of  the  core  be  quadrupled,  the  attraction  of  the 
iron  is  augmented  sixteenfold.     In  fact,  the  attraction  is 


ELECTRO-MAGNETIC  ATTRACTIONS.  141 

proportional,  not  to  the  strength  simply,  but  to  the 
strength  multiplied  by  itself,  or  to  the  square  of  the 
strength  of  the  electro-magnet. 

We  must  be  very  clear  as  to  the  cause  of  this  action, 
and  must,  therefore,  contrast  for  a  moment  the  magnetic 
action  of  hard  steel  with  that  of  soft  iron. 

42.  Soft  iron  is  easily  magnetized,  but  it  loses  its  mag- 
netism when  the  magnetizing  force  is  withdrawn.     Steel 
is  magnetized  with  difficulty,  but  it  retains  its  magnetism 
even  after  the  withdrawal  of  the  magnetizing  magnet. 

43.  This  obstinacy  on  the  part  of  steel  in  declining  to 
accept  the  magnetic  state,  and  this  retentiveness  on  the 
part  of  steel  when  the  magnetic  condition  has  been  once 
imposed  upon  it,  are  called  coercive  force.     It  is  not  a 
happy  term,  but  it  is  the  one  employed. 

44.  Supposing  a  piece  of  magnetized  steel  to  possess  a 
coercive  force  so  high  as  to  resist  further  magnetization, 
its  attraction  by  an  electro-magnet  would  be  directly  pro- 
portional, not  to  the  square  of  the  strength,  but  simply  to 
the  strength  of  the  electro-magnet. 

45.  Why,  then,  does  the  iron  follow  the  law  of  the 
square  of  the  strength  ?     It  is  because  the  magnetic  con- 
dition of  the  iron  is   not   constant,  but  rises  with  the 
strength  of  the  magnet.     When  the  magnetism  of  the 
core  is  doubled,  the  magnetism  of  the  iron  is  also  doubled ; 
when  the  magnetism  of  the  core  is  trebled,  the  magnetism 
of  the  iron  is  trebled.     The  resultant  attraction  is  found 
by  multiplying  the  magnetism  of  the  iron  by  the  magnet- 
ism of  the  core,  and  this  product  is  the  expression  of  the 
law  of  squares  just  referred  to. 

46.  To  make  the  matter  clearer,  let  us  figure  the  mag- 
netism of  the  core  as  due  to  particles  of  magnetism,  which 
are  introduced  into  the  core  in  gradually-increasing  num- 
bers.    Let  us  start  with  a  core  possessing  one  magnetic 


142  NOTES  ON  ELECTKICITY. 

particle,  and  let  it  act  upon  a  piece  of  hard  steel  also  pos- 
sessing one  magnetic  particle;  the  resulting  attraction  will 
be  unity  or  1.  Let  two  particles  be  now  thrown  into  the 
core :  the  steel  in  virtue  of  its  coercive  force  remains  un- 
changed, but  its  particle  being  now  pulled  by  two  parti- 
cles instead  of  one,  the  resulting  attraction  will  be  2.  If 
three  particles  of  magnetism  be  thrown  into  the  core,  all 
of  them  pulling  at  the  single  particle  of  the  steel  will  pro- 
duce a  treble  attraction,  and  so  on. 

47.  ISTow  let  us  start  with  a  core  possessing,  as  before, 
a  single  particle  of  magnetism,  and  with  a  piece  of  iron 
also  possessing  a  single  particle  generated  by  the  core ; 
the  attraction,  as  before,  is  here  unity.     On  introducing 
two  particles  into  the  core,  they  generate  immediately  two 
particles  in  the  iron.     But  two  particles  each  pulled  by 
twice  the  force  first  exerted,  makes  the  attraction  four 
times  what  it  was  at  the  outset. 

It  is  to  be  remembered  that  every  particle  is  attracted 
as  if  the  other  particles  were  absent. 

48.  In  like  manner,  if  three  particles  be  thrown  into 
the  core,  three  particles  are  also  generated  in  the  iron. 
Each  of  these  iron  magnetic  particles  is  pulled  by  the  three 
particles  of  the  electro-magnet ;  that  is  to  say,  each  of  the 
iron  particles  is  pulled  with  three  times  the  primitive  force. 
But  there  are  three  particles  so  pulled ;  hence  the  attrac- 
tion is  nine  times  what  it  was  at  the  outset. 

49.  Let  us  compare  this  action  for  a  moment  with  that 
of  gravity.     Two  masses  of  matter  attract  each  other  with 
a  force  which  we  shall  take  as  our  unit.     If  the  one  mass 
be  doubled,  the  attraction  is  doubled ;  if  both  masses  be 
doubled,  the  attraction   is   increased  fourfold.      If    one 
mass  be  trebled,  the  attraction  is  trebled ;  if  both  masses 
be  trebled,  the  attraction  is  increased  ninefold.     When, 
therefore,  both  the  masses  are  doubled  and  trebled,  we 


INFERENCE  FROM  LAW   OF  SQUARES.  143 

have  the  law  of  squares.  Now,  it  is  this  doubling  and 
trebling,  in  both  cases,  of  the  thing  which  causes  magnetic 
attraction,  which  causes  it  to  follow  the  same  law. 

Inference  from  Law  of  Squares :  Theoretic  Notions. 

50.  Why  do  I  lead  you  through  these  considerations  ? 
Simply  to  make  clear  to  you,  that  if  "  the  law  of  squares  " 
here  developed  show  itself  in  the  action  of  a  magnet  upon 
matter,  we  may  infallibly  infer  that  the  condition  of  that 
matter  is  not  a  constant  condition ;  but  that  it  rises  and 
falls  with  the  condition  of  the  magnet.     Matter  thus  af- 
fected is  said  to  be  magnetized  by  influence  or  by  induc- 
tion.    It  is  attracted  or  repelled  (for  we  shall  come  im- 
mediately to  the  repulsion  of  matter  by  a  magnei)  in  virtue 
of  some  condition  into  which  it  is  temporarily  thrown  by 
the  influencing  magnet. 

51.  What  then  is  the  thing  that  causes  magnetic  attrac- 
tion?    The  human  mind  has  long  striven  to  realize  it. 
Thales  (600  B.  c.)  thought  that  the  magnet  possessed  a 
soul.     Cornelius  Gemma  in  1535  supposed  invisible  lines 
to  stretch  from  the  magnet  to  the  attracted  body,  a  con- 
ception which  reminds  us  of  Faraday's  Lines  of  Force. 
Others   thought   the   iron  the  natural  nutriment   of  the 
magnet.     Descartes  embraced   magnetic  phenomena   in 
his  celebrated  theory  of  vortices,  and  in  our  day  Clerk 
Maxwell  has  worked  in  this  direction.     ^Epinus  assumed 
the  existence  of  a  magnetic  fluid.     Coulomb  assumed  the 
existence  of  two  fluids,  each  self-repellent,  but  mutually 
attractive.     Ampere  deemed  a  magnet  an  assemblage  of 
minute  electric  currents,  which  circulated  round  the  atoms 
of  the  magnetized  body.     These  conceptions  are  some- 
times exceedingly  useful  as  a  means  of  connection  and 
classification,  even  when  we  do  not  believe  them  true. 
William  Thomson    deduces   magnetic  phenomena   from 


144  NOTES  ON  ELECTRICITY. 

"  imaginary  magnetic  matter,"  thus  giving  the  mind  tne 
conception  while  distinctly  releasing  it  from  belief.  The 
real  origin  of  magnetism  is  yet  to  be  revealed. 

Diamagnetism :  Magne-  Crystallic  Action. 

52.  Brugmans,  in  1778,  first  observed  the  repulsion  of 
bismuth  by  a  magnet.     In  1827  Le  Baillif  described  the 
repulsion  of  antimony.     Saigey,  Seebeck,  and  Becquerel, 
also  observed  certain  actions  of  the  kind. 

53.  In  1845  Faraday  generalized  these  observations 
by  demonstrating  the  magnetic  condition  of  all  matter. 
He  showed  that  bodies  divided  themselves  into  two  great 
classes,  the  one  attracted,  the  other  repelled  by  the  poles 
of  a  magnet. 

54.  To  the  force  producing  this  repulsion,  Faraday  gave 
the  name  of  Diamagnetism. 

What  is  the  nature  of  this  force  ?     Is  it  inherent  and 
constant,  or  is  it  induced  ? 

55.  The  repulsion  of  diamagnetic  bodies  follows  accu- 
rately the  law  of  squares  above  developed.     A  double 
force  produces  a  quadruple  repulsion  ;  a  treble  force  pro- 
duces a  ninefold  repulsion,  and  so  on. 

56.  Hence  we  may  infer,  with  certainty,  that  the  con- 
dition of  diamagnetic  bodies  in  virtue  of  which  they  are 
repelled  by  a  magnet,  is  a  condition  induced  by  the  mag- 
net, rising  and  falling  as  the  strength  of  the  magnet  rises 
and  falls. 

57.  The  force  of  diamagnetism  is  vastly  feebler  than 
that  of  ordinary  magnetism.     Of  all   diamagnetic   sub- 
stances, for  example,  bismuth  is  the  most  strongly  repelled ; 
but  its  repulsion  is  almost  incomparably  less  than  the  at- 
traction of  iron.     According  to  Weber,  the  magnetism  of 
a  thin  bar  of  iron  exceeds  the  diamagnetism  of  an  equal 
mass  of  bismuth  about  two  and  a  half  million  times. 


FRICTIONAL  ELECTTJCITY.  145 

58.  Diamagnetic  bodies   under  magnetic   excitement 
exhibit  a  polarity  the  reverse  of  that  of  magnetic  bodies. 
In  all  cases,  whether  we  operate  with  helices  or  with 
magnets,   or  with  helices   and   magnets   combined,   the 
actions  of  magnetic   and   diamagnetic   bodies   are  anti- 
thetical. 

59.  An  iron  statue  standing  erect  on  the  earth's  sur- 
face is  converted  into  a  magnet  by  the  earth's  magnetism ; 
a  marble  statue,  or  a  man  standing  erect,  is  converted  by 
the  same  force  into  a  diamagnet ;  for  marble  is  diamag- 
netic, and  so  are  all  the  tissues  and  all  the  solids  and 
fluids  of  the  human  body.     The  poles  of  the  man  are  those 
of  the  iron  statue  reversed. 

60.  Organic  bodies,  and  most  crystals,  are  magnetized 
with  different  degrees  of  intensity  in  different  directions. 
They  are  endowed  with  axes  of  magnetic  induction. 

61.  Thus  in  the  case  of  Iceland  spar  (carbonate  of 
lime),  the  repulsion  along  the  axis  is  a  maximum.     In  the 
case  of  carbonate  of  iron,  a  crystal  of  the  same  shape  and 
structure  as  carbonate  of  lime,  the  attraction  along  the 
axis  is  a  maximum. 

62.  The  position  assumed  by  a  crystal  when  suspended 
between  the  poles  of  a  magnet,  depends  on  its  magnetie 
axes. 

Frictional  Electricity :  Attraction  and  Repulsion :    Con- 
duction and  Insulation. 

63.  By  the  friction  of  a  woollen  cloth  amber  is  en- 
dowed with  the  power  of  attracting  light  bodies.     This 
substance  was  called  Electron  by  the  Greeks ;  hence  the 
name  Electricity  was  applied  to  the  power  of  attraction 
exhibited  by  amber.     This  attraction  remained  an  isolated 
fact  for  more  than  2,000  years. 

64.  In  the  year  1600  Dr.  Gilbert  of  Colchester,  physi- 

7 


146  NOTES  ON  ELECTRICITY. 

cian  to  Queen  Elizabeth,  showed  that  the  power  of  attrac- 
tion was  shared  by  many  other  substances.  Dry  glass, 
for  example,  when  rubbed  by  silk,  and  dry  sealing-wax 
when  rubbed  by  flannel,  exhibit  this  attractive  power. 
When  they  do  so  they  are  said  to  be  electrified. 

65.  An  electrified  body  attracts  and  is  attracted  by  all 
kinds  of  unelectrified  matter ;  but  repulsion  may  also  come 
into  play.     Thus,  rubbed  glass  repels  rubbed  glass,  and 
rubbed   sealing-wax   repels    rubbed    sealing-wax ;    while 
rubbed  glass   attracts  rubbed  sealing-wax,  and  rubbed 
sealing-wax  attracts  rubbed  glass. 

66.  Hence  the  notion  of  two  kinds  of  electricity:  one 
proper  to  vitreous  bodies,  and  therefore  called  vitreous 
electricity ;  the  other  proper  to  resinous  bodies,  and  there- 
fore called  resinous  electricity. 

67.  These  terms  are  improper;  because  by  employing 
suitable  rubbers  we  can  obtain  the  electricity  of  sealing- 
wax  from  glass,  and  the  electricity  of  glass  from  sealing- 
wax.     We  now  use  the  term  positive  electricity  to  denote 
that  developed  on  glass  by  the  friction  of  silk ;  and  nega- 
tive electricity  to  denote  that  developed  on  sealing-wax 
by  the  friction  of  flannel. 

68.  Bodies  endowed  with  the  same  electricity  repel 
each  other,  while  bodies  endowed  with  opposite  electrici- 
ties attract  each  other.     This  is  the  fundamental  law  of 
electric  action. 

69.  The  rubber  and  the  body  rubbed  are  always  en- 
dowed with  opposite  electricities.     They  always  attract 
each  other.     The  work  done  in  overcoming  this  attraction 
appears  as  heat  in  the  electric  spark. 

70.  To  find  the  kind  of  electricity  with  which  a  body 
is  endowed  we  must  ascertain,  by  trial,  the  electricity  by 
which  the  body  is  repelled.     This,  we  mayi)e  sure,  is  the 
electricity  of  the  body.     Attraction  does  not  furnish  a 
safe  test,  because  unelectrified  bodies  are  attracted. 


THEORIES  OF  ELECTRICITY.  147 

71  Some  substances  possess  in  a  very  high  degree  the 
capacity  of  transmitting  the  electric  power,  or  condition  ; 
others  possess  in  a  high  degree  the  capacity  of  intercept- 
ing it.  The  former  bodies  are  called  conductors,  the  latter 
bodies,  insulators. 

12.  The  insulators  were  formerly  called  electrics,  be- 
cause they  could  be  electrified  by  friction  when  held  in 
the  hand.  The  conductors  were  called  non-electrics,  be- 
cause they  could  not  be  so  electrified.  The  division  is 
improper,  because  if  a  conductor  be  insulated  it  can 
readily  be  electrified.  To  keep  it  electrified  an  insulator 
must  be  introduced  between  it  and  the  earth. 

Theories  of  Electricity :  JZZectric  Fluids. 

73.  What  is  electricity?    Why  should  it  adhere  so 
tenaciously  to  some  substances,  and  flow  so  freely  through 
or   along   others  ?      The  human  mind   has   made  many 
attempts  to  imagine  the  inner  cause  of  electric  action,  and 
it  still  continues  to  make  such  attempts.     Formerly  it  was 
thought  that  magnetism  and  electricity,  as  well  as  light 
and  heat,  were  all  the  work  of  "  imponderable  matter," 
associated  with  the  ordinary  matter.     In  the  case  of  light 
and  heat,  this  conception  has  undergone  profound  modi- 
fication ;  and  we  seem  to  see  clearly  the  mechanical  cause 
of  both.     But  no  similar  clearness  has  as  yet  been   at 
tained  with  regard  to  electricity,  though  a  strong  presump- 
tion exists  that  our  notions  of  it  are  destined  soon  to 
undergo  a  modification  equally  profound. 

74.  Meanwhile  we  may  employ  the  provisional  con- 
ception furnished  by  the  theory  of  electric  fluids.     It  will 
enable  us  to  classify  our  facts,  though  it  is  not  to  be  re- 
garded as  demonstrated. 

75.  According  to  this  theory,  electrical  attractions  and 
repulsions  arise  from  two   invisible   fluids,  each    self-re- 


. 


148  NOTES  ON  ELECTRICITY. 

pulsive  but  both  mutually  attractive.  The  fluids  are 
supposed  to  be  mixed  together  to  form  a  compound  neu- 
tral fluid  in  unelectrified  bodies. 

76.  The  act  of  electrification,  by  friction,  consists  in 
the  forcible  separation  of  the  two  fluids,  one  of  which  is 
diffused  over  the  rubber,  and  the  other  over  the  body 
rubbed.     But  they  may  also  be  separated  in  another  way 
now  to  be  illustrated. 

Electric  Induction :  the  Condenser :  the  jElectrophorus. 

77.  If  an  electrified  body  be  brought  near  an  insulated 
unelectrified  conductor,  but  not  into  contact  with  it,  the 
electrified  body  will  decompose  the  compound  fluid  of  the 
conductor ;  attracting  one  of  its  constituents  and  repelling 
the  other.     When  the  electrified  body  is  withdrawn,  the 
separated  fluids  reunite  and  neutralize  each  other. 

78.  This  forcible  separation   of  the  two  fluids  of  a 
neutral  conductor,  by  the  mere  proximity  of  an  electrified 
body,  is  called  electric  induction.     Bodies  in  this  state  are 
also  said  to  be  electrified  by  influence.     Neutral  bodies  are 
attracted  because  they  are  first  excited  by  induction. 

79.  When  an  insulated  conductor  is  acted  on  by  an 
electrified  body,  its  repelled  electricity  is  free,  but  its 
attracted  electricity  is  held  captive  by  the  inducing  elec- 
trified body.     Connecting  the  conductor  for  a  moment 
with  the  earth,  its  free  electricity  escapes ;  and  then,  on 
the  removal  of  the  electrified  inducing  body,  the  captive 
electricity  is  liberated  and  diffused  over  the  surface  of  the 
conductor. 

80.  Thus  by  the  mere  proximity  of  the  electrified  body, 
and  without   establishing   contact  between   it   and  the 
neutral  conductor,  we  can  charge  the  latter  with  the  oppo- 
site electricity. 

81.  Two  sheets  of  tin-foil  (conductors)  being  separated 


THE  ELECTRIC  MACHINE:    THE  LEYDEN-JAR.        149 

from  each  other  by-  a  sheet  of  glass  (an  insulator),  if  one 
sheet  have  electricity  imparted  to  it,  it  will  act  through 
the  glass,  and  decompose  the  neutral  electricity  of  the 
opposite  sheet  attracting  the  one  constituent  and  repelling 
the  other. 

82.  If  the  second  sheet  be  connected  with  the  earth 
"the  repelled  electricity  will  flow  away,  and  we  shall  have 

two  mutually  attractive  layers  of  electricity  separated 
from  each  other  by  the  glass. 

83.  If  the  one  sheet  of  tin -foil  be  united  with  the  other 
by  a  conductor,,  the  two  opposite  electricities  will  flow 
together ;  the  tin-foil  is  then  said  to  be  discharged.     This 
discharge  usually  assumes  the  form  of  a  spark. 

84.  If  the  surface  of  a  cake  of  resin,  or  of  a  sheet  of 
vulcanized  india-rubber  be  electrified,  a  plate  of  metal 
laid  upon  it  will  have  its  neutral  fluid  decomposed ;   its 
positive  fluid  being  attracted  and  its  negative  repelled. 
On  touching  the  metal  plate  its  free  (repelled)  electricity 
flows  to  the  earth  ;  and  now  if  the  plate  be  raised  by  an 
insulating  handle,  it  will  appear  charged  with  positive 
electricity.     This  is  the  principle  of  the  Electrophorus. 

TJie  Electric  Machine :  the  Ley  den-jar. 

85.  An  Electric  Machine  consists  of  two  parts  :    the 
insulator,  which  is  excited  by  friction,  and  the  prime  con- 
ductor. 

86.  The  first  electric  machine  consisted  of  a  ball  of 
sulphur,  which  was  rubbed  against  the  hand.     It  was  in- 
vented by  Otto  von  Guericke,  burgomaster  of  Magdeburg, 
in  the  year  1671.     A  sphere  of  glass  was  afterward  intro- 
duced, then  a  cylinder  of  glass,  and  finally  a  round  glass 
plate,  which  was  rubbed  with  dry  silk. 

87.  The  prime  conductor  is  thus  charged:  When  the 
glass  plate  is  turned  by  a  handle  it  passes  between  the  silk 


150  NOTES  ON  ELECTEICITY. 

rubbers  and  is  positively  electrified.  The  electrified  glass 
then  acts  by  induction  upon  the  prime  conductor,  attract- 
ing the  negative  electricity  and  repelling  its  positive. 
The  conductor  is  furnished  with  points,  from  which  the 
negative  electricity  streams  out  against  the  excited  glass. 
Thus  the  prime  conductor  is  charged,  not  by  directly 
communicating  to  it  positive  electricity,  but  by  robbing 
it  of  its  negative,  the  positive  remaining  behind. 

88.  The  arrangement  mentioned  in  Note  81  is  virtually 
a  Leyden-jar.     Were  the  plate  of  glass  there  referred  to 
moulded  into  the  shape  of  a  jar,  one  sheet  of  foil  would 
cover  its  interior  and  the  other  its  exterior.     When  the 
jar  is  connected  with  an  electric  machine,  its  charged  in- 
terior coating  acts  by  induction  across  the  glass  on  the 
exterior  coating,  attracting  the  opposite  and  repelling  the 
similar  electricity. 

89.  In  the   experiment  which   led   to    the  discovery 
of  the  Leyden-jar  the  hand  of  the  experimentalist  served 
as  the  outer  coating.  „ 

90.  The  escape  of  the  repefl^d  electricity  of  the  outer 
coating  to  the  earth  leaves  the  cVptive  electricity  exposed 
solely  to  the  attraction  of  that  within  the  jar,  and  enables 
the  jar  to  take  a  strong  charge. 

The  Electric  Current. 

91.  When  the  outer  and  the  inner  coatings  are  con- 
nected by  a  conductor,  an  electric  current  passes  from  the 
one  to  the  other. 

92.  The  current  starts  at  the  same  instant  from  the 
inner  and  outer  coatings;  the  middle  point  of  the  conduct- 
or being  reached  last  by  the  current.     This  indicates  that 
there  are  two  currents  which  start  at  the  same  moment 
from  the  inner  and  outer  coatings. 


THE  ELECTRIC  DISCHARGE.  151 

93.  It  is  agreed  to  call  the   direction  in  which  the 
positive  electricity  flows  the  direction  of  the  current. 

The  Electric  Discharge :  Thunder  and  Lightning. 

94.  "When  an  electric  current  encounters  resistance  in 
its  passage,  heat  is  developed :  this  heat  is  sometimes  so 
intense  as  to  reduce  metals  to  a  state  of  vapor. 

95.  When  a  body  is  intensely  electrified,  it  will  dis- 
charge its  electricity  to  an  unelectrified  body  across  an 
interval  of  air  in  the  form  of  an  electric  spark.      Two 
bodies  oppositely  electrified  discharge  to  each  other  in  the 
same  way. 

96.  When  two  oppositely  electrified  clouds  discharge 
toward  each  other,  the  track  of  the  lightning  marks  the 
course  of  an  electric  current,  and  the  sound  of  the  thunder 
is  the  sound  of  an  electric  spark. 

97.  An  electrified  cloud,  if  it  'come  near  the  earth,  may 
discharge  its  electricity  to  the  earth  jn  the*same  way. 

98.  If  the  body  througli  which  the  atmospheric  elec- 
tricity passes  be  a  good  conductor,  and  of  sufficient  size, 
no  harm  is   done;   but  the  resistance  offered  by  trees, 
houses,  and  animals,  to  the   passage  of  the   electricity 
usually  causes  their  destruction. 

99.  The  nervous  system  Acquires  a  certain  interval  of 
time  to  become  conscious  of  pain.     The  time  of  an  electric 
discharge  is  but  a  small  fraction  of  this  interval ;  hence 
as  a  sentient  apparatus  the  nervous  system  is  destroyed 
before  consciousness  can  set  in.    If  this  be  true — and  there 
are  the  strongest  grounds  for  believing  it  to  be  true — 
death  from  lightning  must  be  painless. 

100.  When  an  electrified  cloud  passes  over  a  pointed 
lightning-conductor,  the  opposite  electricity  of  the  earth 
is  discharged  from  the  point  of  the  conductor  against  the 


152  NOTES  ON  ELECTRICITY. 

cloud.      The  cloud  is  thus  neutralized,  and,  in  general, 
without  producing  thunder. 

101.  The  duration  of  an  electric  spark  amounts  only  to 
an  extremely  small  fraction  of  a  second.     On  this  account, 
when    moving  bodies  are    suddenly  illuminated  by  the 
spark  from  a  Ley  den-jar,  they  appear  to  rest  for  a  short  in- 
terval in  the  position  which  they  occupied  when  the  flash 
fell  upon  them.     A  moving  cannon-ball  illuminated  by  a 
flash  of  lightning  appears  to  stand  still  about  one-eighth 
of  a  second,  this  being  about  the  interval  during  which  an 
impression,  once  made,  persists  upon  the  retina. 

102.  The  unretarded  electric  spark  will  scatter  gun- 
powder, but  will  not  ignite  it.     To  produce  ignition  it  is 
necessary  to  retard  the  discharge  by  sending  it  through  a 
wet  string. 

Electric  Density  :  Action  of  Points. 

103.  If  we  double  the  quantity  of  electricity  imparted 
to  the  same  conductor,  the  density  of  the  electricity  is 
said  to  be  doubled ;  if  we  treble  the  quantity,  the  density 
is  said  to  be  trebled  ;  and  so  on. 

104.  On  a  sphere  the  density  of  the  electricity  is  the 
same  at  all  points  of  its  surface ;  on  a  plate  the  density 
is  greatest  at  the  edges ;  and  on  an  elongated  conductor 
the  density  is  greatest  at  the 'ends. 

105.  When  the  conductor  ends  in  a  sharp  point  the 
electric  density  at  the  point  is  so  great  that  the  electricity 
discharges  itself  into  the  air. 

106.  The  air  thus  electrified  is  self-repellent,  and  is  also 
repelled  by  the  point,  the  so-called  "  electric  wind  "  being 
produced. 

107.  By  causing  an  electric  wind  to  issue  from  opposite 
points  of  a  light  body,  the  reaction  of  the  two  winds 


RELATION  OF  VOLTAIC  TO  FRICTIONAL  ELECTRICITY.  153 

may  make  the  body  to  float  in  stable  equilibrium  in  the 
air. 

Relation  of  Voltaic  to  Frictional  Electricity. 

108.  The  outer  ends  of  two  pieces  of  zinc  and  platinum, 
partially  immersed  in  acidulated  water,  are  in  opposite 
electrical  conditions.     The  free  platinum  end  shows  posi- 
tive electricity,  while  the  free  zinc  end  shows  negative 
electricity. 

109.  When  both  plates  are  united  by  a  wire,  the  posi- 
tive flows  along  the  wire  toward  the  negative,  and  the 
negative   toward  the    positive.      But,  as    mentioned  in 
Note  93,  it  is  agreed  to  call  the  direction  in  which  the 
positive  electricity  flows  the  direction  of  the  current. 

110.  The  force  which  urges  this  current  forward  (the 
electro-motive  force)  is  enormously  less  than  that  which 
urges  forward  a  current  of  frictional  electricity.      The 
consequence  -is,  that  the  latter  is  able  to  surmount  resist- 
ances which  are  totally  un surmountable  by  the  former. 

111.  But  by  linking  cells  together  we  cause  the  voltaic 
current  to  approach  more  and  more  to  the  character  of 
the  frictional  current.     It  requires,  however,  a  battery  of 
more  than  a  thousand  cells  to  make  the  current  from  a 
voltaic  battery  jump  over  an  interval  of  air  I6*00th  of  an 
inch  in  length.     An  electric  machine  of  moderate  power, 
and  furnished  with  a  suitable  conductor,  is  competent  to 
urge  its  current  across  an  interval  ten  thousand  times  as 
great  as  this. 

112.  The   electric   spark  passes  through   air  by  the 
agency  of  the  particles  of  the  conductor  from  which  it 
springs,  and  which  are  carried  forward  by  the  discharge. 

113.  But  measured  by  other  standards  the  frictional 
current  is  almost  incomparably  more  feeble  than  the  vol- 
taic  current.      For   example:  it  is  not  without  special 


154  NOTES  ON  ELECTRICITY. 

arrangements  for  multiplying  the  effect  that  the  current 
from  a  large  electrical  machine  is  enabled  to  deflect  a  mag- 
netic needle. 

114.  Faraday  immersed  two  wires,  the  one  of  zinc  and 
the  other  of  platinum,  each  -^th  of  an  inch  in  diameter,  in 
a  cell  of  acidulated  water.     The  depth  of  immersion  was 
only  -|ths  of  an  inch,  and  the  time  of  immersion  only  J^ths 
of  a  second.     Still  he  found  that  the  electricity  generated 
by  this  small  apparatus,  in  this  brief  time,  produced  a 
distinctly  greater  effect  upon  a  magnetic  needle  than  28 
turns  of  the  large  electric  machine  of  the  Royal  Institu- 
tion. 

115.  A  cubic  inch  of  air,  if  compressed  with  sufficient 
power,  may  be  able  to  rupture  a  very  rigid  envelope  ;  while 
a  cubic  yard  of  air,  if  not  so  compressed,  may  exert  but 
a  feeble  pressure  upon  the  surfaces  which  bound  it.     Now 
the  electricity  of  the  machine  is  in  a  condition  analogous 
to  the  compressed  air.     Its  density,  or,  as  it  fs  sometimes 
called,  its  intensity,  or  tension,  is  great.     The  electricity 
from  the  voltaic  battery,  on  the  other  hand,  resembles  the 
uncompressed  air.      It  exceeds  enormously  in  quantity 
that  from  the  machine ;  but  it  falls  enormously  below  it 
in  intensity. 

116.  The  deflection  of  a  magnetic  needle  and  other 
actions  of  the  voltaic  current  depend  solely  upon  quantity, 
hence  the  vast  superiority  of  the  voltaic  current  in  pro- 
ducing such  deflection. 

117.  Faraday  found  the  quantity  of  electricity  dis- 
engaged by  the  decomposition  of  a  single  grain  of  water 
in  a  voltaic  cell  (see  Note  5)  to  be  equal  to  that  liberated 
in  800,000  discharges  of  the  great  Leyden  battery  of  the 
Royal  Institution.     This,  if  concentrated  in  a  single  dis- 
charge, would  be  equal  to  a  great  flash  of  lightning.     He 
also  estimated  the  quantity  of  electricity  liberated  by  the 


HISTORIC  JOTTINGS.  155 

chemical  action  of  a  single  grain  of  water  on  four  grains 
of  zinc  to  be  equal  in  quantity  to  that  of  a  powerful 
thunder-storm. 

118.  Weber  and  Kohlrausch  have  found  that  the  quan- 
tity  of  electricity   associated  with  one  milligramme  of 
hydrogen  in  water,  if  diffused  over  a  cloud  1,000  metres 
above  the  earth,  would  exert  upon  an  equal  quantity  of 
the  opposite  electricity  at  the  earth's  surface  an  attractive 
force  of  2,268,000  kilogrammes.* 

Historic    Jottings^   concerning    Conduction    and    the 
Leyden-jar. 

119.  In  1729,  Stephen  Grey,  pensioner  of  the  Charter 
House,  discovered  electric  conduction.     Connecting  an  end 
of  a  wire  700  feet  long  with  a  glass  tube  and  supporting 
the  wire  on  loops  of  silk,  he  found  that  on  rubbing  the 
tube  the  distant  end  of  his  wire  became  electrified  and 
attracted  light  bodies.    He  also  found  that  a  wire  loop  did 
not  answer  as  a  support,  as  the  electricity  escaped  through 
it ;  hence  arose  the  division  of  bodies  into  conductors  and 
insulators.     Grey's  observations  were  written  down  by 
the  secretary  of  the  Royal  Society  the  day  before  his 
death. 

120.  In  October,  1 745,  Von  Kleist,  a  bishop  of  Cammin, 
in  Pomerania,  charged  with  electricity  a  flask  containing 
sometimes  mercury,  sometimes  alcohol.     Through  a  cork 
in  the  neck  of  the  flask  passed  an  iron  nail,  which  was 
brought  into  contact  with  the  conductor  of  an  electrical 
machine.     On  touching  the  nail  Yon  Kleist  experienced  a 
violent  shock. 

121.  In  January,  1746,  Cunseus  of  Leyden  received  also 
a  shock,  and  his  experiment  was  repeated  by  Allamand 

*  The  metre  is  a  yard  and  one-eleventh  in  length ;  the  milligramme 
is  -GL5th  of  a  grain  ;  the  kilogramme  is  2  Ibs.  3^  oz. 


156  NOTES  ON  ELECTRICITY. 

and  Musschenbroek.  A  wire  passed  from  the  conductor 
of  the  machine  into  a  flask  filled  with  water.  Musschen- 
broek held  the  flask  in  the  right  hand,  the  machine  was 
turned,  and  then  with  the  left  hand  he  drew  a  spark  from 
the  conductor.  The  shock  received  was,  according  to 
Musschenbroek  so  terrible,  that  he  declared  he  would  not 
receive  a  second  for  the  crown  of  France.  Musschen- 
broek observed  that  it  was  only  the  person  who  held  the 
flask  in  his  hand  that  felt  the  shock.  Kleist  failed  to 
recognize  this  condition. 

122.  In  Germany  the  jar  is  sometimes  called  Kleist's 
jar,  but  more  commonly,  because  of  the  failure  just  referred 
to,  the  Ley  den-jar.      The  theory  of  it,  and  other  similar 
apparatus,  was  given  by  Franklin  in  September,  1747. 
(See  Notes  81,  88,  89,  90.) 

123.  In  1747,  Dr.  Watson,  Bishop  of  Llandaff,  sent  the 
discharge  from  a  Leyden-jar  through  2,800  feet  of  wire, 
and  through  the  same  distance  of  earth.     Subsequently,  in 
the  same  year,  he  sent  the  discharge  through  10,600  feet 
of  wire,  supported  by  insulators  of  baked  wood.     The  ex- 
periment was  made  on  Shooter's  Hill. 

124.  In  1748  similar  experiments  were  made  by  Frank- 
lin across  the  Schuylkill,  and  by  De  Luc  across  the  Lake 
of  Geneva. 

Historic  Jottings^  concerning  the  Electric  Telegraph. 

125.  The  first  proposal  of  an  electric  telegraph  was 
made  by  an  anonymous  contributor  to  the  Scot's  Maga- 
zine for  17 53.     Various  attempts  to  apply  frictional  elec- 
tricity for  this  purpose  were  subsequently  made.     They 
culminated  in  the  exceedingly  ingenious  arrangement  of 
Mr.  (now  Sir  Francis)  Ronalds,  published  in  1823. 

126.  The  voltaic  pile  was  described  by  Volta  in  a 
letter  to  Sir  Joseph  Banks,  written  from  Como  in  1800. 


HISTORIC  JOTTINGS.  157 

127.  Immediately  afterward   Nicholson   and   Carlisle 
discovered  the   decomposition   of  water  by  the  voltaic 
current. 

128.  In  1808  Sommering  proposed  a  system  of  tele- 
graphy based  on  the  discovery  of  Nicholson  and  Carlisle. 
A  similar  system  was  proposed  about  the  same  time  by 
Prof.  Coxe,  of  Pennsylvania. 

129.  In  1820  GErsted  discovered  the  deflection  of  a 
magnetic  needle  by  an  electric  current.* 

130.  The  idea   of   employing  the   deflection   of   the 
needle  for  telegraphic    purposes   occurred  to   the   cele- 
brated French  mathematician,  La  Place;    the   problem 
was  partly  worked  out  by  Ampere,  and  still  further  ad- 
vanced by  Ritchie,  Professor  of  Natural  Philosophy  in  the 
Royal  Institution. 

131.  In  1832  Baron  Schilling  constructed  models  of  a 
telegraphic  apparatus  which  were  exhibited  before  the 
Emperors  Alexander  and  Nicholas. 

132.  In  1833  Gauss  and  Weber  established  an  electric 
telegraph  between  the  Physical  Cabinet  and  the  Astro- 
nomical and  Magnetic  Observatories  of  Gottingen,   em- 
bracing a  distance  of  nearly  10,000  feet.     Faraday's  elec- 
tricity instead  of  Volta's  was  employed  by  Gauss  and 
Weber. 

133.  Steinheil  was  requested  by  Gauss  to  pursue  the 
subject.     To  the  telegraph  he  made  many  highly-impor- 

*  In  his  exceedingly  useful  little  book  on  the  Telegraph,  published  in 
Weale's  "Rudimentary  Series,"  Mr.  Robert  Sabine  quotes  the  following 
remarkable  passage  from  a  work  on  magnetism,  published  in  Paris,  by 
Prof.  Izarn,  in  1804:  "D'apres  les  observations  de  Romagnesi,  physicien 
de  Trente,  1'aiguille  deja  aimantee,  et  que  1'on  soumet  ainsi  au  courant 
galvanique,  eprouve  une  declinaison;  et  d'apres  celles  de  J.  Majon, 
savant  chemiste  de  Genes,  les  aiguilles  non-aimentees  acquierent  par  ce 
moyen  une  sorte  de  polarite  magnetique."  The  work  containing  this 
passage  was  lent  to  Mr.  Sabine  by  Mr.  Latimer  Clark! 


158  NOTES  ON  ELECTRICITY. 

tant  contributions  and  suggestions.  In  1837  lie  had  estab- 
lished a  system  of  wires  about  40,000  feet  in  length,  con- 
necting various  points  in  the  city  of  Munich  and  its 
neighborhood.  The  most  considerable  discovery  of  Stein- 
lieil,  and,  indeed,  one  of  the  most  practically  important 
hitherto  made  in  connection  with  telegraphy,  is  that  the 
"  return  wire  "  between  two  stations  might  be  dispensed 
with,  and  the  earth  employed  in  its  stead. 

134.  In  1834  Wheatstone,  by  means  of  a  rotating  mir- 
ror, made  his  celebrated  experiments  on  the  velocity  of 
electricity.     In  the  following  year  he  exhibited  one  of 
BarOn   Schilling's   telegraphs  in  his   lectures   at  King's 
College. 

135.  In  1836  Mr.  William  Fothergill  Cooke  saw  in  the 
lectures  of  Prof.  Muncke,  at  Heidelberg,  the  performance 
of  a  similar  instrument.     Struck  by  its  obvious  practical 
importance,  he  devised  a  system  of  telegraphy,  and,  in 
partnership  with  Wheatstone,  dating  from  June,  1837, 
succeeded  in  introducing   the   telegraphic    system  into 
England. 

136.  From  1832  to  1836  Morse  sought  to  apply  chemi- 
cal decomposition  by  the  electric  current  to  telegraphic 
purposes;    he   abandoned   this   for  his    electro-magnetic 
system  devised  in  1836.     This  method  consists  in  stamp- 
ing, by  means  of  the  attraction  of  an  electro-magnet,  dots 
and  lines  upon  a  slip  of  paper  caused  to  move  by  proper 
mechanism  over  the  circumference  of  a  wheel. 

137.  In  1850  the  first  submarine  cable  was  laid  by 
Mr.  Brett  between  Dover  and  Calais.     It  survived  only  a 
day.     In  1851  another  cable  was  laid  down,  which  proved 
successful. 

138.  On  the  5th  of  August,  1858,  the  submergence  of 
the  first  Atlantic  cable  was  completed,  and  messages  were 
sent  between  England  and  America.     The  cable  ceased 


PHENOMENA  IN   TELEGRAPH-CABLES.  159 

to  act  on  the  4th  of  September,  or  about  a  month  after  its 
submersion. 

139.  In  1865  the  second  Atlantic  cable  was  laid  and 
lost.     In  1866  a  cable  was  successfully  laid,  and  in  the 
same  year  the  cable  of  1865  was  recovered.    Messages  are 
now  sent  between  England  and  America  at  the  rate  of 
fourteen  words  a  minute. 

Phenomena  observed  in  Telegraph-  Cables* 

140.  Davy  showed  ("Elements  of  Chemical  Philoso- 
phy," 1812,  p.  154)  that  a  Leyden-battery  could  be  charged 
with  voltaic  electricity.* 

*  Davy  thus  describes  the  celebrated  battery  with  which  he  made 
this  experiment.  The  spirit  to  which  the  battery  owed  its  birth  has  not 
diminished  among  the  members  of  the  Royal  Institution :  "  The  most 
powerful  combination  that  exists  in  which  number  of  alternations  is  com- 
bined with  extent  of  surface,  is  that  constructed  by  the  subscriptions  of 
a  few  zealous  cultivators  and  patrons  of  science,  in  the  laboratory  of  the 
Royal  Institution  (in  1808).  It  consists  of  two  hundred  instruments, 
connected  together  in  regular  order,  each  composed  of  ten  double  plates 
arranged  in  cells  of  porcelain,  and  containing  in  each  plate  thirty-two 
square  inches ;  so  that  the  whole  number  of  double  plates  is  2,000,  and 
the  whole  surface  128,000  square  inches.  This  battery,  when  the  cells 
were  filled  with  60  parts  of  water  mixed  with  one  part  of  nitric  acid, 
and  one  part  of  sulphuric  acid,  afforded  a  series  of  brilliant  and  im- 
pressive effects.  When  pieces  of  charcoal  about  an  inch  long  and  one- 
sixth  of  an  inch  in  diameter,  were  brought  near  each  other  (within  the 
thirtieth  or  fortieth  part  of  an  inch)  a  bright  spark  was  produced,  and 
more  than  half  the  volume  of  the  charcoal  became  ignited  to  whiteness, 
and  by  withdrawing  the  points  from  each  other  a  constant  discharge 
took  place  through  the  heated  air,  in  a  space  equal  at  least  to  four 
inches,  producing  a  most  brilliant  ascending  arch  of  light,  broad,  and 
conical  in  form  in  the  middle.  When  any  substance  was  introduced 
into  this  arch,  it  instantly  became  ignited ;  platina  melted  as  readily  in 
it  as  wax  in  the  flame  of  a  common  candle ;  quartz,  the  sapphire,  mag- 
nesia, lime,  all  entered  into  fusion ;  fragments  of  diamond,  and  points 
of  charcoal  and  plumbago,  rapidly  disappeared,  and  seemed  to  evapo- 


1GO  NOTES  ON  ELECTRICITY. 

141.  Dr.  Werner  Siemens  was  the  first  to  employ  (in 
1847)  gutta-percha  as  a  means  of  insulating  subterranean 
telegraph-wires.     On  the  18th  of  January,  1850,  in  a  paper 
communicated  to  the  Physical  Society  of  Berlin,  he  stated 
that  a  subterranean  wire  covered  with  gutta-percha,  and 
surrounded  by  the  moisture  of  the  earth,  behaved  like  a 
colossal  Leyden-jar.      He  also  found  that  ordinary  tele- 
graph-wires charged  themselves,  though  in  a  much  smaller 
degree  than  the  subterranean  wires. 

142.  In  1838  Faraday  predicted  the  retardation  of  the 
electric  discharge  by  its  own  inductive  action.     ("  Experi- 

rate  in  it,  even  when  the  connection  was  made  in  a  receiver  exhausted 
by  the  air-pump  ;  but  there  was  no  evidence  of  their  having  previously 
undergone  fusion. 

"  When  the  communication  between  .the  points  positively  and  nega- 
tively electrified  was  made  in  air,  rarefied  in  the  receiver  of  the  air- 
pump,  the  distance  at  which  the  discharge  took  place  increased  as  the 
exhaustion  was  made,  and  when  the  atmosphere  in  the  vessel  supported 
only  one-fourth  of  an  inch  of  mercury  in  the  barometrical  gauge,  the 
sparks  passed  through  a  space  of  nearly  half  an  inch ;  and  by  withdraw- 
ing the  points  from  each  other,  the  discharge  was  made  through  six 
or  seven  inches,  producing  a  most  beautiful  coruscation  of  purple  light, 
the  charcoal  became  intensely  ignited,  and  some  platina  wire  attached 
to  it,  fused  with  brilliant  scintillations,  and  fell  in  large  globules  upon 
the  plate  of  the  pump.  All  the  phenomena  of  chemical  decomposition 
were  produced  with  intense  rapidity  by  this  combination.  When  the 
points  of  charcoal  were  brought  near  each  other  in  non-conducting  fluids, 
such  as  oils,  ether,  and  oxymuriatic  compounds,  brilliant  sparks  occurred, 
and  elastic  matter  was  rapidly  generated  ;  and  such  was  the  intensity  of 
the  electricity,  that  sparks  were  produced,  even  in  good  imperfect  con- 
ductors, such  as  the  nitric  and  sulphuric  acids. 

"  When  the  two  conductors  from  the  ends  of  the  combination  were 
connected  with  a  Leyden-battery,  one  with  the  internal,  the  other  with 
the  external  coating,  the  battery  instantly  became  charged,  and  on  re- 
moving the  wires,  and  making  the  proper  connections,  either  a  shock  or 
a  spark  could  be  perceived  ;  and  the  least  possible  time  of  contact  was 
sufficient  to  renew  the  charge  to  its  full  intensity." 


PHENOMENA   IN  TELEGRAPH-CABLES.  161 

mental  Researches,"  1333.     "Faraday  as  a  Discoverer," 
new  edition,  p.  89.) 

143.  In  1854  Faraday  experimented  with  cables  at 
the  gutta-percha  works  of  the  Electric  Telegraph  Company. 
One  hundred  miles  of  gutta-percha  covered  wire  were  im- 
mersed in  water,  and  a  second  hundred  miles  of  a  similar 
wire  were  placed  in  a  dry  tank.     We  will  call  the  former 
the  water  wire,  and  the  latter  the  air  wire. 

144.  Connecting  one  pole  of  a  battery  with  the  earth, 
and  connecting  the  other  pole  with  one  of  the  two  insu- 
lated ends  of  the  water  wire,  on  breaking  the  connection 
and  touching  the  wire  a  powerful  shock  was  received ;  the 
discharge  from  the  wire  was  also  competent  to  ignite  a 
Statham  fuze.     When,  after  having  been  in  contact  with 
the  battery,  the  wire  was  separated  and  connected  with 
a  galvanometer,  the  instrument  was  powerfully  affected. 

145.  A  rush  of  electricity  into  the  wire  was  declared 
by  the  galvanometer  when  contact  was  made ;  a  rush  out 
of  the  wire  was  declared  when  the  wire  between  the  bat- 
tery and  the  galvanometer  was  connected  with  the  earth. 
None  of  these  effects  were  observed  with  the  100  miles  of 
air  wire. 

146.  Faraday,  like  Werner  Siemens,  rightly  explained 
the  effect  by  likening  the  cable  to  an  enormous  Leyden- 
jar,  the  wire  constituting  the  interior,  the  water  the  ex- 
terior coating,  with  the  gutta-percha  insulator  between 
them.     In  fact,  the  surface  of  the  wire  in  these  experi- 
ments amounted  to  8,300  square  feet,  while  the  surface  of 
the  outer  coating  of  water  was  33,000  square  feet.     To  the 
charge  and  discharge  of  this  apparatus  the  effects  observed 
were  due. 

147.  In  a  subterranean  line  of  telegraph  1,500  miles 
long  were  placed  three  galvanometers :  one,  «,  at  the  be- 
ginning of  the  wire ;  a  second,  #,  in  the  middle ;  and  a 


162  NOTES  ON  ELECTRICITY. 

third,  c,  at  the  end,  which  was  also  connected  with  the 
earth. 

148.  Connecting  the  battery  with  the  wire  of  the  galva- 
nometer a,  that  instrument  was  instantly  affected ;  after 
a  sensible  time  b  was  affected ;  and  after  a  still  longer 
time,  c.     It  required,  in  fact,  two  seconds  for  the  electric 
stream  to  reach  the  last  instrument. 

149.  All  the  instruments  being  deflected,  when  the 
battery  was  suddenly  cut  off  at  a,  that  instrument  in- 
stantly fell  to  zero,  b  fell  subsequently,  and  c  after  a  still 
longer  interval. 

150.  By  a  brief  touch  of  the  battery-pole  against  #, 
that  instrument  was  deflected,  and  could  be  allowed  to 
fall  back  into  its   neutral   condition  before  the  electric 
power  had  reached  b  /  b  in  its  turn  would  be  affected,  and 
left  neutral  before  the  power  had  reached  c. 

151.  In  this  case  a  wave  of  force  was  sent  into  the  wire 
which  gradually  travelled  along  it,  appearing  in  different 
parts  of  the  wire  at  successive  intervals  of  time. 

152.  It  was  even  possible,  by  adjusted  touches  of 
the  battery,  to  make  several  successive  waves  coexist  in 
the  wire. 

153.  When,  after  making  and  breaking  contact  at  a, 
that  galvanometer  was  connected  with  the  earth,  part 
of  the  electricity  sent  into  the  wire  returned,  and  de- 
flected a  in  the   reverse  direction ;  here  currents  flowed 
in  opposite  directions  out  of  both  extremities  of  the  wire. 

154.  These  effects  of  induction  enabled  Werner  Sie- 
mens and  Faraday  to  explain  the  widely-different  veloci- 
ties assigned  by  different  experimenters  to  the  electric 
current. 

155.  To  pass  through   any  conductor  electricity  re- 
quires time,  the  time  being  directly  proportional  to  the 
lengtJi  of  the  conductor. 


ARTIFICIAL  CABLES.  163 

156.  But  in  the  case  of  a  submarine  cable  another  cause 
of  retardation  comes  into  play,  namely,  the  charging  of 
the  cable;    the  retardation  here  is  proportional   to   the 
square  of  the  length  of  the  cable. 

Artificial  Cables. 

157.  It  was  to  illustrate  points  like  these  and  to  deter- 
mine the  dimensions  to  be  given  to  the  Atlantic  cables, 
that  Mr.  Cromwell  Yarley  devised  his  artificial  cables. 

158.  In  one  of  these  cables  a  resistance  equal  to  that 
of  a  real  cable  14,000  miles  in  length  is  obtained  by  intro- 
ducing into   the  path  of  the   current   feebly-conducting 
liquids  instead  of  metallic  wires.     The  inductive  action 
is  obtained  by  means  of  condensers  of  tin-foil.     In  another 
artificial  cable  coils  of  wire  are   employed  to  give  the 
necessary  resistance. 

159.  The  arrangement  described  in  Note  81  is  a  con- 
denser.    But  those   constructed   by  Mr.  Varley  are   of 
enormously  greater   area,  the   condensing   sheets   being 
separated  from  each  other  not  by  plates  of  glass,  but  by 
thin  sheets  of  paper  and  paraiBne.     The  vastness  of  the 
area  and  the  proximity  of  the  inducing  surfaces  combine 
to  exalt  the  effect. 

160.  When  the  condensers  themselves  are  charged  by 
a  battery,  on  discharging  them  they  exhibit  phenomena 
similar  to  those  of  a  Leyden-jar.     The  shock,  spark,  and 
other  effects  of  frictional  electricity,  are  readily  obtained. 

161.  A  series  of  50  condensers,  for  example,  joined  "  in 
cascade,"  that  is  to  say,  with  the  outer  coating  of  each 
joined  to  the  inner  coating  of  the  next,  when  charged  with 
a  battery  of  1,000  cells,  yield  powerful  sparks,  and  defla- 
grate wires. 

162.  If  the  wire  be  bent  and  introduced  into  a  glass  of 
water,  the  glass  is  shattered  by  the  discharge. 


1G4  NOTES  ON   ELECTRICITY. 

163.  In  the  14,000-mile  artificial  cable  are  introduced 
a  series  of  eleven  tubes  containing  the  resisting  liquid. 
Into  these  dip  wires.     One  end  of  the  charging  battery  is 
connected  with  the  earth,  and  the  other  end  can,  at  will, 
be  connected  with  the  artificial  cable.     A  series  of  ten 
galvanometers  are   placed   between   the   resisting  tubes 
along  the  artificial  cable. 

164.  When  no  condensers  are  employed,  on  making 
connection  with  the  battery  all  the  galvanometers  appear 
to  be  simultaneously  deflected. 

165.  When  the  condenser  is  introduced  between  each 
pair  of  resisting  cells — ten  condensers  in  all — the  current 
has  to   charge   each   condenser  to  a  certain  degree  be- 
fore it  can  sensibly  affect  the  galvanometer  beyond  the 
condenser.      Hence,  when  the  condensers  are  attached, 
the  action  on  the  galvanometers  is  successive,  not  con- 
temporaneous. 

166.  Mr.  Varley  supposed   his    14,000-mile    artificial 
cable  divided  into  sections  representing  stations  in  Lon- 
don, at  Gibraltar,  Malta,  Suez,  Aden,  Bombay,  Calcutta, 
Rangoon,   Singapore,   Java,  and  Australia.      Supposing 
an  actual  cable  laid,  and  galvanometers  placed  at  these 
stations,  the  deflections  obtained  on  establishing  battery 
contact  would  be  successive.     They  are  represented  by 
the  deflections  of  the  galvanometers  associated  with  the 
artificial  cable. 

16V.  By  varying  the  resistance  and  the  amount  of  in- 
ductive condenser-surface,  a  representation  of  any  other 
cable  may  readily  be  produced. 

168.  Connected  with  the  needle  of  each  of  the  ten  gal- 
vanometers is  a  reflecting  mirror,  from  which  a  brilliant 
spot  of  light  is  cast  upon  a  screen.  When  the  cable  is  not 
in  action,  the  ten  spots  form  a  row  along  the  same  ver- 
tical line ;  when  the  battery  contact  is  made,  the  successive 


SKETCH   OF  OHM'S  THEORY.  165 

deflections  of  the  galvanometers  is  declared  by  the  suc- 
cessive motion  of  the  spots. 

Sketch  of  Ohm's  Theory  and  KolilrauscK  s  Verification. 

169.  I  have  already  spoken  (Note  110)  of  the  force 
which  urges   forward  the   electric  current   (the  electro- 
motive force).     The  amount  of  this  force  may  be  deduced 
from  the  action  of  the  current,  when  opposed  by  different 
resistances,  upon  a  freely-suspended  magnetic  needle. 

170.  If  the   wire   which   carries  the   current  be   cut 
across,  the  current  ceases  to  flow.     The  electricity  ceases 
to  be  dynamic.     But  at  the  two  ends  of  the  severed  wire 
we  have  static  electricity. 

171.  By  suitable  instruments  the  amount  of  this  stati- 
cal charge  may  be  determined ;  it  increases  with  the  num- 
ber of  elements  of  the  battery. 

172.  It  is,  moreover,  proportional  to  the  strength  of 
the  current  obtained  when  the  wires  are  reunited. 

173.  In  this  way  the  statical  charge  becomes  a  meas- 
ure of  dynamical  action :  electricity  at  rest  is  connected 
with  electricity  in  motion. 

174.  In  experiments  on  the  electroscopic  properties  of 
the  voltaic  circuit  it  is  necessary  that  the  battery  should 
be  well  insulated. 

175.  If  the  middle  point  of  a  wire  which  connects  the 
two  poles  of  a  voltaic  battery  be  connected  with  the  earth, 
the  tension  of  that  point  is  null.     The  circuit  gradually 
rises  in  tension   right  and  left  to  the  two  poles  of  the 
battery.     But  on  one  side  of  the  point  we  have  exclusive- 
ly positive  electricity,  while  at  the  other  side  we  have  ex- 
clusively negative  electricity. 

176.  At  equal  distances,  at  opposite  sides  of  the  zero- 
point,  the  tension  is  the  same. 

177.  If  any  other  point  than  the  middle  be  connected 


166  NOTES  ON   ELECTRICITY. 

at  the  earth,  it  becomes  the  zero-point,  right  and  left  of 
which  as  before  we  have  the  two  opposite  electricities. 

178.  If  the  negative  end  of  the  battery  be  connected 
with  the  earth,  the  whole  wire  shows  positive  electricity ;  if 
the  positive  end  be  connected  with  the  earth,  the  whole 
wire  shows  negative  electricity. 

179.  The  wire  offers  a  certain  resistance  to  the  passage 
of  the  current.     The  battery  itself  is  also  in  the  circuit, 
and  the  current  has  to  overcome  its  resistance  also.     But 
the    resistance  of   the  battery  may  be  expressed  by  a 
certain  length  of  the  external  wire.     When  this  is  done 
the  sum  of  the  lengths  of  both  wires  is  called  the  reduced 
length  of  the  circuit. 

180.  Given  the  reduced  length  of  the  circuit  and  the 
electro-motive  force,  we  can  determine"  by  a  simple  calcula- 
tion the  electric  tension  of  every  point  in  the  circuit. 

181.  The  circuit  through  which  the  current  flows  may 
be  represented  by  a  horizontal  line  (called  an  abscissa) ; 
the  electric  tension  at  every  point  of  the  circuit  may  be 
represented  by  a  vertical  line  (called  an  ordinate).     If 
ordinates  be  drawn  to  represent  the  electric  tensions  at  a 
great  number  of  points  of  the  circuit,  the  line  joining  the 
ends  of  all  the  perpendiculars  will  represent  the  distribu- 
tion  of  electric  tension  in   the    circuit.      The    steepness 
of  this  line  also  represents  what  Ohm  called  the  electric 
fall. 

182.  More  strictly,  the  electric  fall  is  the  decrease  in 
the  length  of  the  ordinate  for  the  unit  of  length  of  the 
abscissa. 

183.  The  total  charge  of  the  wire  is  expressed  by  the 
area  of  the  triangle  enclosed  by  the  ordinate,  abscissa, 
and  line  of  fall. 

184.  The  laws  of  the  voltaic  circuit  as  enunciated  by 
Ohm,  have  been  verified  everywhere.     The  electroscopic 


SKETCH  OF   OHM'S  THEORY.  167 

state  of  the  circuit  has  been  examined  by  Kohlrausch,  and 
found  to  be  in  strict  accordance  with  Ohm's  theory. 

185.  Ohm  assumed  the  passage  of  the  electric  fluid 
from  one  section  to  another  of  the  connecting  wire  to  be 
due  solely  to  the  difference  of  electric  tension  between  the 
two  sections  ;  he  further  assumed  the  quantity  of  electri- 
city transmitted  to  be  proportional  to  this  difference  of 
tension,  and  from  these  fundamental  assumptions  he  de- 
duced the  laws  of  the  voltaic  circuit. 

186.  These  laws  may  be  briefly  stated  thus  : 

«.  The  strength  of  the  current  is  directly  proportional 
to  the  electro-motive  force. 

b.  The  strength  of  the  current  is   inversely  propor- 
tional to  the  resistance. 

c.  If  the  wire  which  unites  the  two  poles  of  battery  be 
of  the  same  material,  and  of  the  same  thickness  through- 
out, the  "  electric  fall "  is  the  same  throughout  the  wire. 

d.  If  the  wire  be  of  the  same  material,  but  of  different 
thicknesses,  the  "  fall "  is  steeper  on  the  thin  wire  than  on 
the  thick.     The  "  fall "  is  inversely  proportional  to  the 
cross-section  of  the  wire. 

e.  If  the  poles  be  connected  by  two  wires  of  the  same 
thickness,  but  of  different  resisting  powers,  the  electric 
fall  is  steepest  on  the  more  resisting  wire.     The  "  fall "  is 
directly  proportional  to  the   specific  resistances   of  the 
wires. 

187.  In  verifying  these  laws  Kohlrausch  employed  a 
condenser  to  augment  the  feeble  charges  obtained  from 
his  voltaic  cell,  and  he  held  this  instrument  to  be  essential. 
By  an  exceedingly  skilful  device  Sir  Wm.  Thomson  has 
rendered  the  condenser  unnecessary,  and  has  thus  greatly 
simplified  the  means  of  demonstration. 


168  NOTES  ON  ELECTRICITY. 

Electro-chemistry. —  Chemical  Actions  in  the  Voltaic  Cell: 
Origin  of  the  Current. 

188.  Philosophers  suppose  matter  to  be  made  of  ele- 
mentary parts  called  atoms,  which  are  practically  indi- 
visible. 

189.  The  elementary  atoms  can  be  caused  to  unite  to 
form  compound  atoms,  which  are  called  molecules. 

190.  Thus  water  is  formed  of  the  combination  of  the 
atoms  of  oxygen  and  hydrogen ;  common  salt  is  formed  of 
union  of  atoms  of  chlorine  and  sodium ;  potash  is  formed 
by  the  union  of  the  atoms  of  potassium  and  oxygen  ;  the 
sulphuric  acid  also  which  we  employed  to  acidulate  our 
water  is  formed  by  the  union  of  atoms  of  sulphur  with 
atoms  of  oxygen. 

191.  When,  as  in  our  first  experiment,  two  strips  of 
zinc  and  platinum  are  dipped  into  acidulated  water,  the 
zinc,  as  we  know,  exerts  a  very  strong  attraction  on  the 
oxygen  of  the  water.     When  the  strips  are  united  this 
attraction  triumphs ;  the  oxygen  unites  with  the  zinc,  and 
a  voltaic  current  is  established.     . 

192.  The  oxide  of  zinc  here  formed  combines  with  the 
sulphuric  acid  and  forms  sulphuric  zinc. 

193.  By  this  removal  of  the  oxide  from  its  surface  the 
zinc  is  kept  constantly  clean,  and  thus  enabled  to  attract 
other  atoms    of  oxygen    from   the    surrounding  liquid. 
During  this  process  the  zinc  gradually  dissolves,  and  as 
long  as  this  continues  the  electric  current  will  flow.     In 
fact,  it  is  the  constant  dissolution  of  the  zinc  that  main- 
tains the  permanent  current. 

194.  The  hydrogen  of  the  water,  as  we  have  seen, 
escapes  as  a  free  gas  from  the  surface  of  the  platinum, 
which,  unlike  the  zinc,  is  not  dissolved. 

195.  We  are  not  yet  quite  clear  as  to  the  precise  way 


ELECTRO-CHEMISTRY.  169 

in  which  the  electric  current  is  supported  by  the  solution 
of  the  zinc,  but  the  following  facts  and  speculations  ought 
to  be  known  to  you. 

196.  When  two  different  metals  are  brought  into  con- 
tact, with  no  liquid  between  them,  one  of  them  charges 
itself  with  positive  and  the  other  with  negative  electricity. 
We  have  here  the  famous  "  contact  force  "  which  Volta 
and  his  followers  considered  to  be  the  urging  power  of  the 
voltaic  current. 

197.  But  the  generation  of  heat,  and  the  performance 
of  mechanical  work,  by  the  mere  contact  of  two  metals, 
would  be  equivalent  to  a  perpetual  motion.     It  would  be 
at  variance  with  the  law  which  requires  for  the  production 
of  any  power  an  equivalent  consumption  of  some  other 
power. 

198.  It  is,  however,  a  fact  that  when  two  different 
metals  touch  each  other  the  positive  electricity  resorts  by 
preference  to  one  metal,  and  the  negative  electricity  to 
the  other ;  the  two  electricities  are  as  it  were  attracted 
differently  by  the  two  metals. 

199.  This  difference  of  attraction,  however,  only  causes 
a  momentary  rearrangement   of   the   two    electricities, 
which  pass,  when  the  contact  is  made,  into  a  new  condi- 
tion of  equilibrium.     As  long  as  the  contact  continues  this 
equilibrium  is  not  disturbed ;  there  is  no  continuous  cur- 
rent. 

200.  We  may  regard  the  distinct  atoms  which  enter 
into  the  molecules  of  a  compound  as  charged  in  a  similar 
manner.     For  example,  the  atoms  of  hydrogen  and  oxygen 
when  they  unite  to  form  a  molecule  of  water,  may  be 
looked  upon  as  charged  like  the  two  touching  metals. 
This  would  be  the  case  if  the  atoms,  like  the  metals,  pos- 
sessed different  attractions  for  the  two  electricities. 

201.  When  strips  of  zinc  and  platinum  are  plunged 


170  NOTES  ON  ELECTRICITY. 

in  such  a  liquid,  the  positively-charged  atofn  will  turn 
toward  the  one  metal,  and  the  negatively-charged  atom 
toward  the  other. 

202.  But,  unless  the  metals  touch  each  other,  electrical 
equilibrium  immediately  sets  in,  a  constant  state  of  electric 
tension  being  set  up  at  the  free  ends  of  the  two  metals. 

203.  The  electricity  at  the  ends  may  be  permitted  to 
flow  into  a  condenser,  and  may  be  thus  stored  up ;  such  a 
condenser  may  thus  be  discharged  through  a  covered  wire 
which  passes  round  a  magnetic  needle,  a  deflection  of  the 
needle  being  thus  produced. 

204.  Thus  in. Davy's  experiment  with  his  large  voltaic 
battery,  wherewith  he  charged  his  battery  of  Leyden-jars, 
the  latter,  after  having  been  charged,  might  be  discharged 
through  a  galvanometer,  a  magnetic  deflection  being  thus 
produced. 

205.  But  the  metals,  once  relieved  of  their  charge, 
would  immediately  reload  themselves  with  electricity,  and 
might  be  again  employed  to  charge  a  Leyden  battery,  and 
to  produce  a  deflection  of  a  magnetic  needle. 

206.  At  no  moment  during  this  process  the  battery 
circuit  would  be  complete ;  still  we  should  have  a  succes- 
sion of  magnetic  actions  similar  to  those  observed  with  a 
closed  circuit. 

207.  In  fact,  in  the  closed  circuit  the  solution  of  the 
zinc  incessantly  removes  the  charged  surface  of  that  metal 
by  dissolving  it  away,  and  enables  the  zinc  to  take  a  fresh 
charge ;  an  incessant  effort,  never  fully  satisfied,  is  made 
to  establish  electric  equilibrium ;  the  incessant  renewal  of 
the  effort  maintains  the  electric  current. 

Chemical  Actions  at  a  Distance :  Electrolysis. 

208.  Thus,  then,  in  the  cell  where  the  voltaic  current 
is  generated  chemical  action  occurs.    We  have,  on  the  one 


CHEMICAL  ACTIONS  AT  A  DISTANCE.  171 

hand,  the  decomposition  of  the  water,  and  on  the  other  the 
combination  of  the  zinc  with  the  oxygen  and  the  sulphu- 
ric acid. 

209.  But  a  voltaic  current  can  also  produce  chemical 
action  at  a  distance  from  its  place  of  generation.     This 
discovery,  as  stated  in  Note  127,  was  made  in  the  year 
1800  by  Nicholson  and  Carlisle. 

210.  We  cannot  decompose  water  by  a  single  voltaic 
cell ;  but  when  two  or  more  cells  are  united  to  form  a 
battery,  the   current  from   such   a  battery,   when   sent 
through  acidulated  water,  tears  asunder  the  united  atoms 
of  oxygen  and  hydrogen. 

211.  The  oxygen  is  set  free  at  the  place  where  the 
current  enters ;    the  hydrogen   is  set  free  at  the  place 
where  the  current  quits  the  liquid.     If  the  direction  of  the 
current  be  reversed,  the  oxygen  and  hydrogen  instantly 
change  places. 

212.  It  must  be  clearly  borne  in  mind  that  the  direc- 
tion of  the  current,  as  already  defined,  is  the  direction  in 
which  the  positive  electricity  moves.     Knowing,  therefore, 
the  places  at  which  the  oxygen  and  hydrogen  are  liber- 
ated, we  can  infer  with  certainty  the  direction  of  the  cur- 
rent through  the  liquid. 

213.  For  every  volume  of  oxygen  liberated  in  the  de- 
composition of  water  by  a  voltaic  current,  two  volumes  of 
hydrogen  are  set  free. 

214.  Electro-chemical  decomposition  is  called  electro- 
lysis /  and  the  compound  liquid  decomposed  by  the  elec- 
tric current  is  called  an  electrolyte. 

215.  The  electric  current  formed  a  powerful  means  of 
analysis  in  the  famous  experiments  of  Sir  Humphry  Davy 
in  1807. 

216.  By  operating  with  the  current  upon  ordinary 
potash,  Davy  found  the  base  of  this  substance  to  be  a 


172  NOTES  ON  ELECTRICITY. 

metal  of  exceeding  lightness,  and  with  an  extraordinary 
appetite  for  oxygen.  When  placed  on  water,  it  floated 
on  the  liquid,  and  combined  with  its  oxygen.  By  the 
heat  thus  generated  the  liberated  hydrogen  was  caused  to 
burst  into  flame.  When  a  globule  of  the  metal  was  placed 
on  ice,  it  burned  with  a  bright  flame,  and  the  hole  made 
by  the  heat  was  filled  with  a  solution  of  potash. 

217.  Soda,  treated  in  the  same  manner,  also  yielded  a 
metal  resembling  that  of  potash.     Thus  Davy,  by  the  use 
of  the  voltaic  current,  decomposed  the  alkaline  earths,  and 
greatly  expanded  our  knowledge  of  chemistry. 

218.  To  obtain  these  effects  it  is  necessary  to  bring  the 
potash  and  the  so.da  to  a  state  of  fusion  by  heat.     In  the 
solid  state  they  are  non-conductors  of  electricity.     In  fact, 
the  molecules,  when  rigid,  cannot  turn  in  the  manner  in- 
dicated in  Note  201.     To  conduct  the  current,  it  is  neces- 
sary that  they  should  thus  turn  and  be  decomposed. 

219.  When  the  current  is  sent  through  a  solution  of 
common  salt,  it  decomposes  both  the  water  and  the  salt. 
The  chlorine  of  the  salt,  in  company  with  the  oxygen  of 
the  water,  appears  where  the  current  enters  the  liquid. 
The  sodium  of  the  salt,  in  company  with  the  hydrogen  of 
the  water,  appears  where  the  current  quits  the  liquid. 

220.  Chlorine  possesses  powerful  bleaching  properties  ; 
and  if  the  solution  of  salt  be  colored  with  indigo  or  litmus, 
the  presence  of  the  chlorine  is  declared  by  the  destruction 
of  the  color. 

221.  When  a  current  is  sent  through  a  solution  of 
iodide  of  potassium,  the  brown  substance  iodine  is  set 
free  where  the  current  enters,  while  the  metal  potassium 
is  set  free  where  the  current  quits  the  solution.     The  ex- 
periment may  be  made  by  moistening  bibulous  paper  with 
the  dissolved  iodide. 

222.  In  electrolysis  it  is  usual  to  immerse  two  plates  of 


ELECTROLYSIS.  173 

platinum,  or  of  some  other  suitable  substance,  in  the 
liquid  to  be  decomposed,  and  to  send  the  current  from 
plate  to  plate.  The  plate  at  which  the  current  enters  the 
liquid  is  called  the  Positive  Electrode,  the  plate  at  which 
the  current  quits  the  liquid  is  called  the  Negative  Elec- 
trode. Without  the  liquid  these  electrodes  would,  as  we 
have  already  learned,  charge  themselves  with  positive 
and  negative  electricity. 

223.  But  inasmuch  as  electricities  which  attract  each 
other  are   of  opposite  qualities,  the  substance  which  is 
liberated  at  the  positive  electrode  is  called  the  Electro- 
ISTegative  constituent,  while  the  substance  liberated  at  the 
negative  electrode  is  called  the  Electro-Positive  constitu- 
ent of  the  liquid. 

224.  Thus,  in  the  examples  above  given  the  oxygen, 
chlorine,  and  iodine,  are  the  electro-negative  elements ;  the 
hydrogen,  sodium,  and  potassium,  being  the  electro-posi- 
tive elements. 

225.  The  terms   electro-positive  and  electro-negative 
are,  however,  relative,  for  a  substance  may  be  electro- 
positive in  one  combination,  and  electro-negative  in  an- 
other. 

226.  If  an  electric  current  be  conducted  through  a 
solution  of  sulphate  of  soda,  it  separates  the  sulphuric  acid 
from  the  soda ;  the  presence  of  the  acid  may  be  proved  by 
its  turning  a  vegetable  color  red. 

227.  When  nitrate  of  silver  or  acetate  of  lead  is  decom- 
posed by  a  voltaic  current,  crystals  of  silver,  or  of  lead, 
are  deposited  on  the  negative  electrode. 

228.  The  chemical  actions  of  the  electric  current,  some 
examples  of  which  are  here  given,  constitute  what  is  called 
Electro-chemistry. 

229.  Electro-plating  and  gilding  and  the  electrotype 
process  are  important  applications  of  electro-chemistry. 


174  NOTES  ON  ELECTRICITY. 

Here  a  chemical  compound  containing  gold,  silver,  or 
copper,  is  decomposed  by  a  voltaic  current,  the  metal 
being  deposited  on  the  surface  intended  to  be  coated 
with  it. 

230.  If  the  surface  on  which  the  metal  is  deposited 
have  a  design  engraved  upon  it,  the  lines  of  the  engrav- 
ing are  accurately  filled  by  the  metal  which,  when  the 
deposit  is  thick  enough,  may  be  detached,  a  perfect  copy 
of  the  design  being  thus  obtained. 

Measures  of  the  Electric  Current. 

231.  The  tangent-compass,  devised  by  Weber,  con- 
sists of  a  vertical  ring  of  brass  or  copper,  in  the  centre  of 
which  swings  a  small  compass-needle.     The  ring  being 
placed  in  the  magnetic  meridian,  the  needle  is  deflected 
when  a  current  is  sent  round  the  ring.     The  strength  of 
the  current  can  be  proved  to  be  proportional  to  the  tan- 
gent of  the  angle  of  deflection ;  hence  the  name  of  the 
instrument. 

232.  The  voltameter  is  an  instrument  devised  by  Fara- 
day to  measure  the  strength  of  an  electric  current.     It 
consists  of  a  graduated  tube  which  receives  and  measures 
the  quantity  of  gas  generated  by  the  current  in  a  given 
time. 

233.  The  strengths  of  a  series  of  currents  measured  by 
the  voltameter  are  accurately  proportional  to  the  same 
strengths  measured  by  the  tangent-compass.     Placing  a 
tangent-compass  and  a  voltameter  in  the  same  series  of 
circuits,  the  tangents  of  the  angles  observed  in  the  one 
case  are  accurately  proportional  to  the  quantities  of  gas 
generated  in  the  other. 


ELECTRIC  POLARIZATION.  175 

Electric  Polarization :  Hitter's  Secondary  Pile. 

234.  When  an  electric  current  is  sent  through  acidu- 
lated water  a  film  of  oxygen  covers  the  positive  electrode, 
and  a  film  of  hydrogen  covers  the  negative  electrode. 
One  of  these  two  substances  being  electro-positive,  and  the 
other  electro-negative,  they  act  in  the  liquid  like  two  dif- 
ferent metals ;  the  hydrogen  plays  the  part  of  zinc,  and 
the  oxygen  plays  the  part  of  platinum. 

235.  Interrupting   the   primary   battery   circuit,    and 
uniting  together  the  two  plates  covered  with  their  respec- 
tive films,  an  electric  current  is  obtained. 

236.  The  direction  of  this  current  is  from  the  hydro- 
gen film  to  the  oxygen  film  in  the  liquid,  and  from  the 
oxygen  film  to  the  hydrogen  film  through  the  connecting 
wire. 

237.  Two    electrodes    thus    covered  with   condensed 
gaseous  films  are  said  to  be  polarized;  and  the  currents 
obtained  from  them  are  called  currents  of  polarization. 

238.  Now  the  battery   current    being    always   from 
oxygen  to  hydrogen  (see  Note  211),  it  is  plain  that  the 
current  of  polarization  is  always  opposite  in  direction  to 
the  battery  current  employed  to  polarize  the  electrodes. 

239.  When  a  decomposition  cell  with  platinum  plates 
is  introduced  into  a  voltaic  circuit,  it  is  found  that  the 
battery   current,   though   strong   at   starting,   gradually 
sinks.     This  sinking  is  due  to  the  gradual  development 
of  the  antagonistic  current  of  polarization. 

240.  Also  in  the  cells  of  the  battery  itself  this  current 
of  polarization  may  come  prejudicially  into  play.     When 
two  metals,  say  zinc  and  platinum,  and  one  liquid,  say 
acidulated  water,  are  employed,  the  platinum  plate   is 
coated  with  a  film  of  hydrogen. 

241.  This  hydrogen,  being  electro-positive,  resembles 


176  NOTES  ON  ELECTRICITY. 

a  plate  of  zinc,  so  that  when  it  is  present  we  Lave,  as  it 
were,  zinc  opposed  to  zinc  in  the  battery. 

242.  Were  both  plates  actually  of  zinc,  we  could  have 
no  current ;  and  with  the  hydrogen  film  which  approxi- 
mates to  zinc  we  have  only  a  feeble  current.     To   get 
the  full  effect  of  the  zinc  and  platinum  some  means  must 
be  devised  to  remove  from  the  platinum  its  film  of  hy- 
drogen. 

243.  This  is  effected  in  Grove's  battery  by  the  em- 
ployment of  two  liquids.     The  one  is  strong  nitric  acid, 
which  contains  the  plate  of  platinum ;  the  other  is  dilute 
sulphuric  acid,  which  contains  the  plate  of  zinc.     The 
nitric  acid  is  placed  in  a  vessel  of  porous  earthenware, 
which  becomes  saturated  with  the  liquid  and  allows  the 
current  to  pass  through  it. 

244.  When  the  current  passes,  the  hydrogen  liberated 
at  the  platinum  electrode  in  Grove's  cell  is  instantly  oxi- 
dized by  the  nitric  acid,  and  prevented  from  forming  a 
film  upon  the  surface  of  the  platinum. 

245.  If  instead  of  employing  a  single  decomposition 
cell  and  a  single  pair  of  platinum  electrodes,  we  employ  a 
series  of  such  cells,  and  send  the  same  current  through 
them  all,  we  convert  every  pair  of  such  plates  into  an  ac- 
tive voltaic  couple ;  and  if  the  number  of  such  couples  be 
great,  effects  of  great  intensity  may  be  obtained. 

246.  If  instead  of  using  decomposition  cells  we  simply 
employ  a  series  of  plates  of  the  same  metal,  say  a  series 
of  half-crowns,  separated  from  each  other  by  pieces  of 
bibulous  paper  or  by  bits  of  cloth  wetted  with  acidulated 
water ;  on  sending  a  voltaic  current  through  such  a  pile 
of  plates,  we  liberate  on  one  of  the  surfaces  of  each  plate 
a  film  of  oxygen,  and  on  the  other  surface  a  film  of  hydro- 
gen.    These  play  the  part  of  the  two  different  metals  in 
the  pile  of  Yolta. 


FARADAY'S  ELECTROLYTIC  LAW.  177 

247.  The  electro-motive  force  of  such  a  pile  maybe  far 
greater  than  that  of  the  battery  which  charges  it.    It  may 
produce  a  far  more  brilliant  spark,  and  urge  its  current 
against  resistances  which  would  be  quite  insuperable  to 
the  original  battery  current. 

248.  The  discoverer  of  this  form  of  pile  was  Bitter ;  it 
is  sometimes  called  the  secondary  pile,  to  distinguish  it 
from  the  battery  which  charges  it. 

Faraday's  Electrolytic,  Law. 

249.  When  the  self-same  current  is  sent  through  a 
series  of  cells  containing  various  compound  liquids,  the 
same  amount  of  liquid  is  not  decomposed  in  all  cases. 

250.  Let  the  current  be  sent  in  succession  through  a 
series  of  cells  containing  water,  oxide  of  lead,  chloride  of 
lead,  iodide  of  lead,  and  chloride  of  silver ;  then  taking 
them  in  the  above  order,  the  weights  of  the  liquids  de- 
composed are  represented  by  the  numbers  9,  111.5,  139, 
230.5,  143.5. 

251.  The  question  now  is,  how  are  these  weights  of  the 
respective  substances  divided  between  the  two  electrodes? 
Supposing  the  numbers  to  express  grains,  we  should  have 
the  following  division  between  the  electrodes : 

At  the  positive  electrode.  At  the  negative  electrode. 

Water 8       grains  oxygen. ...  1.        grain  hydrogen. 

Oxide  of  lead. . .  8          "          "       103.5  grains  lead. 

Chloride  of  lead.  35.5      "      -chlorine...  103.5      "        " 

Iodide  of  lead..   127      "       iodine 103.5      "         " 

Chloride  of  silver  35.5      "       chlorine...  108         "      silver. 

252.  Now  these  numbers  express  the  combining  pro- 
portions of   the  respective  substances ;    by  the  electric 
current  in  all  cases  the  law  of  combination  as  regards 
quantity  is  exactly  inverted.     The  substances  combine  in 
equivalent  proportions ;  they  are  decomposed  in  precisely 


178  NOTES  ON  ELECTRICITY. 

the  same  proportions.     This  is  the  celebrated  law  of  elec- 
trolysis discovered  by  Faraday. 

253.  In  no  case  in  the  body  of  the  electrolyte  is  any 
decomposition  observed;  in  no  case  is  any  gas  there  liber- 
ated.    The  substances  set  free  appear  at  the  electrodes, 
and  there  alone. 

254.  Taking  water  as  an  illustration,  the  process  is  to 
be  figured  thus :  When  the  electrodes,  charged  with  elec- 
tricity from  the  battery,  are  plunged  into  the  liquid,  the 
oxygen  atom  of  the  water  turns  toward  the  positive,  and 
the  hydrogen  atom  toward  the  negative  electrode. 

255.  If  the  electro-motive  force  be  strong  enough,  the 
oxygen  is  torn  away  from  its  hydrogen ;  the  free  hydro- 
gen immediately  converges   its   attraction  on  the   next 
adjacent  oxygen  atom,  and  unites  with  it,  dislodging  at 
the    same   time   the   hydrogen  with  which   that    atom 
had  been  previously  combined.     Another  atom  of  hydro- 
gen is  thus  liberated,  which  in  its  turn  decomposes  the 
adjacent  water-molecule.      Thus   through  the   chain   of 
molecules  run  a  series  of  decompositions,  followed  by  im- 
mediate recompositions,  until  the  negative  electrode  is 
reached.     Here  the  hydrogen,  having  no  further  oxygen 
with  which  to  combine,  is  liberated  as  a  gas.     This  is  the 
theory  of  Grotthuss,  which  at  all  events  fairly  embraces 
the  facts. 

NobilPs  Iris  Rings. 

256.  The  hardness  of  steel  in  tempering  it  is  judged 
by  its  color,  which  is  due  to  a  film  of  oxide  overspreading 
the  steel.    The  oxide  which  forms  on  the  surface  of  molten 
lead  also  shows  vivid  colors. 

257.  These  are  the  colors  of  thin  plates  investigated 
by  Newton  and  explained  by  Thomas  Young. 

258.  By  electro-chemical  decomposition  Nobili   pro- 


DISTRIBUTION    OF  HEAT  IN  THE   CIRCUIT.  179 

ciuced  such  colors  in  a  very  beautiful* manner.  Placing, 
for  example,  a  polished  steel  plate  in  a  dilute  solution  of 
acetate  of  lead,  and  connecting  the  plate  with  the  positive 
pole  of  a  voltaic  battery,  on  dipping  the  end  of  a  wire 
connected  with  the  negative  pole  into  the  solution,  the 
peroxide  of  lead  is  liberated  on  the  surface  of  the  steel 
immediately  under  the  wire ;  and  a  film  gradually  dimin- 
ishing in  thickness  spreads  from  that  point  outward. 
Round  this  point  we  have  a  series  of  concentric  circles 
showing  vivid  iris  colors. 

259.  These  colors,  like  all  those  of  thin  plates,  depend 
upon  the  thickness  of  the  film,  which  diminishes  as  the 
distance  traversed  by  the  current  increases. 

(Du  Bois-Reymond  has  shown  that  when  the  point 
from  the  negative  end  of  the  battery  is  very  near  the 
steel  plate,  the  thickness  of  the  film  corresponding  to  the 
different  circles  is  inversely  proportional  to  the  cubes  of 
their  radii.) 

Distribution  of  Heat  in  the  Circuit. 

260.  When  the  two  ends  of  a  voltaic  battery  are  con- 
nected by  a  thick  wire  of  good  conducting  material  the 
wire  is  not  sensibly  heated ;  the  heat  due  to  the  oxidation 
of  the  zinc  is  in  this  case  confined  to  the  battery  itself. 

261.  But  if  the  two  ends  of  the  battery  be  connected 
by  a  wire  that  offers  a  resistance  to  the  current,  the  wire 
is  heated,  and  may,  if  properly  chosen,  be  raised  to  a 
white  heat. 

262.  Considering  the  battery  as  the  hearth  where  the 
zinc  is  burnt,  we  might  be  led  to  infer  that  the  heat  due 
to  the  combustion  of  the  zinc  is  liberated  on  the  hearth 
itself,  and  that  its  amount  depends  solely  upon  the  quanti- 
ty of  zinc  consumed. 

263.  This,  however,  is  not  the  case.     Let  the  battery, 


180  NOTES  ON  ELECTRICITY. 

with  its  two  ends  united  by  a  thick  wire,  be  surrounded 
by  a  vessel  of  water,  to  which  the  heat  developed  by  the 
oxidation  say  of  an  ounce  of  zinc  is  communicated ;  the 
quantity  of  heat  developed  is  measured  by  the  rise  of 
temperature  of  the  water. 

264.  Let  the  battery,  with  its  two  ends  united  by  the 
resisting  wire,  be  placed  in  the  same  vessel,  and  let  the 
heat  generated  in  the  battery  by  the  oxidation  of  an  ounce 
of .  zinc  be  again  determined ;  this  heat  will  be  less  than 
that  observed  in  the  last  experiment. 

265.  If  the  connecting  wire  be  now  enclosed  in  a  sepa- 
rate vessel,  and  if  the  heat  generated  in  the  wire  be  thus 
determined,  on  adding  this  amount  of  heat  to  that  lib- 
erated in  the  battery,  a  total  heat  is  obtained  exactly 
equal  to  that  generated  in  the  battery  alone,  when  the 
good  conducting  wire  was  employed. 

266.  In  fact,  the  absolute  amount  of  heat  generated  by 
the  oxidation  of  an  ounce  of  zinc  is  perfectly  constant ; 
but  it  may  be  distributed  in  various  proportions  between 
the  battery  and  the  external  circuit. 

Relation  of  Heat  to  Current  and  to  Resistance. 

267.  On  what  does  heat  developed  in  a  wire  uniting 
the  two  ends  of  a  voltaic  battery  depend  ? 

268.  It  depends,  in  the  first  place,  on  the  strength  of 
the   current,  but  it  is  not   simply  proportional  to  that 
strength. 

269.  Let  the  strengths  of  a  series  of  currents,  deter- 
mined either  by  the  tangent-compass  or  the  voltameter, 
be  represented  by  the  numbers  1,  2,  3,  4,  then  the  quanti- 
ties of  heat  developed  in  the  same  wire  by  these  respec- 
tive  currents  are  expressed  by  the  numbers   1,   4,   9, 
and  16. 


MAGNETO-ELECTRICITY.  181 

270.  The  heat  generated  is  therefore  proportional  to 
the  square  of  the  strength  of  the  current. 

271.  Preserving  the  strength  of  the  current  constant, 
the  heat  generated  is  proportional  to  the  electrical  re- 
sistance of  the  wire  through  which  it  passes.     These  im- 
portant principles  were  established  by  Joule. 

272.  Thus  if  one  of  two  equal  currents  pass  through  a 
silver  wire,  and  the  other  through  a  platinum  wire  of  the 
same  length  and  thickness,  the  heat  generated  in  the 
platinum  will  be  ten  times  that  generated  in  the  silver, 
because  the  resistance  of  the  former  is  ten  times  that  of 
the  latter.     To  urge  the  current  through  the  platinum  in 
this  case  would,  however,  require  greater  battery-power 
than  that  necessary  for  the  silver. 

273.  Hence,  when  the  same  current  is  sent  through  a 
wire  composed  of  alternate  lengths  of  silver  and  platinum 
of  equal  thickness,  the  platinum  spaces  may  be  raised  to 
a  white  heat,  while  the  silver  is  not  raised  to  the  faintest 
glow. 

Magneto-Electricity:  Induced  Currents. 

274.  In  a  conductor  near  to,  but  not  in  contact  with  a 
voltaic  circuit,  a  current  is  aroused  when  the  circuit  is 
established.     "When  the  circuit  is  interrupted  a  current  is 
also  aroused  in  the  conductor. 

275.  Thus,  supposing  the  voltaic  circuit  to  be  bent 
into  the  shape  of  a  ring ;  and  that  a  second  ring,  not  in 
the  circuit,  is  placed  near  the  first :  at  the  completion,  and 
at  the  interruption  of  the  circuit,  a  current  will  run  round 
the  second  ring. 

276.  The  two  currents  in  the  second  ring  are  called 
secondary  currents.     They  are  of  momentary  duration. 
They  impart,  in  passing,  a  shock  to.  a  magnetic  needle 
round  which  they  are  sent,  and  by  the  motion  of  which 


182  NOTES  ON   ELECTRICITY. 

their  existence  is  demonstrated.  But  they  vanish  imme- 
diately, being  quenched  by  the  resistance  of  the  ring  and 
converted  into  heat. 

277.  These  two  momentary  currents  flow  in  opposite 
directions  through  the  ring.     The  secondary  current,  ex- 
cited on  making  the  circuit,  is  opposed  in  direction  to  the 
primary  exciting  current;  that  started  on  interrupting 
the  circuit  flows  in  the  same  direction  as  the  primary. 

278.  These  secondary  currents  are  called  induced  cur- 
rents.    They  were  discovered  by  Faraday  in  1830,  and 
described  by  him  in  his  Philosophical  papers  for  1831. 

279.  If,  instead  of  employing  a  single  ring,  we  make 
use  of  an  electro-magnetic  helix,  every  coil  of  the  helix 
will  furnish  its  quota  of  current,  and  the  sum  total  of  effect 
is  much  greater  than  when  only  a  single  ring  or  coil  is 
employed. 

For  the  following  experiments,  two  flat  spirals,  each 
formed  of  covered  copper  wire,  are  used. 

280.  One  of  the  spirals  is  laid  flat  upon  a  table,  its  two 
ends  being  connected  with  a  galvanometer;   the  other 
spiral  is  connected  with  a  voltaic  battery,  with  which  the 
connection  can  be  established  or  broken  at  pleasure.     Let 
us  call  this  the  inducing  or  primary  spiral,  and  that  con- 
nected with  the  galvanometer  the  secondary  or  induced 
spiral. 

281.  Laying  one  spiral  upon  the  other,  on  sending  a 
current  through  the  primary,  the  needle  of  the  galva- 
nometer is  suddenly  driven  aside  by  the  current  induced 
in  the  secondary ;  but  the  force  which  acts  upon  the  needle 
passes  away  in  an  instant,  the  needle  returning  to  its  first 
position. 

282.  On  interrupting  the  current  the  needle  also  re- 
ceives a  shock,  being  deflected  in  the  opposite  direction. 
It  thus  declares  the  existence  of  a  second  temporary  cur- 


MAGNETO-ELECTRICITY.  1 83 


rent  in  the  secondary  spiral.  The  directions  of  these  two 
currents,  with  reference  to  that  of  the  primary,  have  been 
already  indicated;  Note  277. 

283.  Holding  the  secondary  spiral  at  a  distance  from 
the  primary  with  the  current  flowing  through  the  latter ; 
on  causing  the  secondary  spiral  to  approach  the  primary, 
a. current  is  aroused;  this  current  ceases  the  moment  the 
motion  toward  the  primary  ceases. 

284.  On  withdrawing  the  secondary  spiral  from  the 
primary,  a  current  is  also  aroused;  this  current  also  ceases 
the  moment  the  motion  of  withdrawal  ends. 

285.  The  current  excited  by  approach  is  opposed  in 
direction  to  the  primary ;  the  current  excited  by  with- 
drawal is  in  the  same  direction  as  the  primary. 

286.  Two  electric  currents  flowing  in  the  same  direc- 
tion attract  each  other ;  if  they  flow  in  opposite  directions 
they  repel  each  other. 

287.  Hence,  to  make  the  secondary  spiral  approach  its 
primary,  we  have  to  overcome  a  repulsion  y  while  to  with- 
draw the  secondary  from  the  primary  we  have  to  over- 
come an  attraction.     Thus  in  order  to  produce  these  in- 
duced currents  we  must  expend  mechanical  force. 

288.  The  force  thus  expended  appears  as  heat  in  the 
secondary  wire  after  the  cessation  of  the  induced  current. 
It  is  the  mechanical  equivalent  of  that  heat. 

289.  The  approach  of  a  magnetic  pole  to  the  second- 
ary spiral  and  the  withdrawal  of  the  pole  from  the  same 
spiral  also  arouse  induced  currents.     But,  as  before,  it  is 
only  during  the  periods  of  approach  and  withdrawal  that 
the  current  appears. 

290.  Thus  by  the  mere  motion  of  a  magnet,  and  with- 
out any  battery  or  machine,  electric   currents  may  be 
produced. 

291.  Every  change  of  the  magnetic  condition  of  the 


184  NOTES  ON  ELECTRICITY. 

space  near  a  secondary  coil,  or  within  it,  produces  an  in- 
duced current  in  the  coil.  If  the  change  be  an  augmenta- 
tion of  magnetism,  the  current  is  in  one  direction  ;  if  it  be 
a  diminution  of  magnetism,  the  current  is  in  the  opposite 
direction. 

292.  When  a  long  secondary  coil  surrounds  a  primary 
coil  with  a  core  of  iron,  by  breaking  and  making  the  cir- 
cuit of  the  primary  in  rapid  succession,  a  series  of  power- 
ful discharges  may  be  obtained.     An  automatic  apparatus 
is  usually  employed  to  make  and  break  the  circuit. 

293.  Such  Induction  Coils  have  been  constructed  with 
great  skill  by  Ruhmkorff,  and  are,  therefore,  sometimes 
called  Ruhmkorff 's  coils.    Mr.  Apps  has  recently  produced 
induction  coils  of  astonishing  power. 

294.  The  power  of  a  coil  depends  mainly  on  the  per- 
fection of  the  insulation  of  its  coils.     The  induced  cur- 
rents in  a  Ruhmkorff's  coil  may  possess  thousands  of 
times  the  electro-motive  force  of  the  primary  which  ex- 
cites them.     They  are  able,  for  example,  to  overleap  as 
sparks,  distances  thousands  of  times  greater  than  that 
possible  to  the  primary. 

Relation  of  Induced  Currents  to  the  Lines  of  Magnetic 
Force.     Rotatory  Magnetism. 

295.  The  foregoing  phenomena  and  principles  were  all 
laid  bare  by  Faraday.    He  also  established  most  important 
relations  between  his  induced  currents  and  the  lines  of 
force  surrounding  a  magnet.     See  Note  25. 

296.  He  proved  that  when  a  conductor  moves  along 
the  lines  of  force  no  induced  currents  appear ;  but  that 
when  it  moves  across  the  lines  of  force  such  currents  are 
generated. 

297.  He  proved,  for  example,  that  when  a  metal  disk 


ROTATORY  MAGNETISM.  185 

is  caused  to  rotate  so  as  to  be  tangent  to  the  lines  of 
force,  no  current  appears ;  while  when  the  disk,  in  its  rota- 
tion, cuts  the  lines  of  force,  currents  flow  along  the  disk, 
from  the  centre  to  the  circumference  and  from  the  circum- 
ference to  the  centre.  Closed  circuits  are  thus  established 
in  the  disk. 

208.  This,  in  fact,  is  the  "Magnetism  of  Rotation," 
discovered  by  Arago  in  1820,  which  received  complete 
explanation  at  the  hands  of  Faraday. 

299.  Faraday  showed  that  the  lines  of  force  of  terres- 
trial magnetism  suflice  to  produce  induced  currents  when 
they  are  intersected  by  the  rotating  disk.     In  fact,  all  the 
efiects   of  magneto-electric   induction   may  be   obtained 
from  the  magnetism  of  the  earth. 

300.  When  a  conductor  rotates  round  an  axis  which 
is  parallel  to  the  lines  of  force,  it  experiences  simply  the 
resistance  due  to  the  friction  of  the  air ;  but  if  the  axis 
of  rotation  be  transverse  to  the  lines  of  force,  the  rotation 
is  retarded  by  the  interaction  of  the  magnet  and  the  in- 
duced currents. 

301.  This  retardation  may  become  so  powerful  as  in- 
stantly to  arrest  the  rotation.     If,  for  example,  a  cube  or 
sphere  of   copper  suspended  from  a  twisted  string  be 
caused  to  spin,  by  untwisting,  between  the  poles  of  an  un- 
excited    electro-magnet,   it   experiences   the    retardation 
due  to  air  friction  only ;  but  on  the  supervention  of  the 
magnetic  force  the  rotation  is  suddenly  arrested.     Fara- 
day also  showed  that  in  passing  a  plate  of  copper  rapidly 
to  and  fro  Jbetween  the  magnetic  poles  you  seem  to  be 
cutting  cheese,  though  nothing  is  visible.     It  is  as  if  pure 
space  were  a  kind  of  solid. 

302.  If  by  mechanical  means  the  conductor  be  com- 
pelled to  rotate  or  to  move  to  and  fro  between  the  excited 
poles,  it  will  be  heated.     Joule  first  demonstrated  this ; 


186  NOTES  ON  ELECTRICITY. 

but  a  very  striking  demonstration  of  it  was  given  by 
Foucault,  who  heated  his  celebrated  gyroscope  in  this 
way.  The  heat  is  readily  rendered  sufficiently  intense  to 
melt  fusible  metal.  Between  the  unexcited  poles  no  effect 
of  this  kind  is  produced. 

303.  The   repulsion  set  up  by  induced  currents   be- 
tween the  helices  and  the  moving  masses  of  iron  in  an 
electro-magnetic  engine,  would  of  itself  limit  the  practi- 
cal application  of  electricity  as  a  motive  power.     Never- 
theless, though  such  engines  speedily  reach  the  limit  of 
their  action,  the  conversion  of  molecular  force  into  me- 
chanical effect  may  be  rendered  far  more  perfect  than  in 
the  case  of  the  steam-engine. 

The  JEJxtra-  Current. 

304.  If  the  secondary  coil  of  a  Ruhmkorff's  machine 
have  its  ends  united,  the  secondary  circuit  being  then 
complete,  the  spark  obtained  in  breaking  the  primary  is 
small.     On  separating  the  two  ends  of  the  secondary  the 
primary  spark  is  instantly  augmented. 

305.  The  diminution  of  the  spark  is  due  to  the  reac- 
tion of  the  completed  secondary  circuit  upon  the  primary. 
When  the  secondary  circuit  is  interrupted  this  reaction 
ceases. 

306.  The  primary  circuit  in  its  turn  can,  when  com- 
plete, react  upon  the  secondary.     It  is  complete  when- 
ever contact  is  made  by  the  automatic  contact-breaker. 
A  great  enfeeblement  of  the  secondary  current  is  the 
consequence.     When  the  primary  circuit  is  interrupted 
the  reaction  does  not  exist;    there  is  no  enfeeblement, 
the  full  power  of  the  secondary  being  developed.     It  is 
on  this  account  that  in  Ruhmkorff's  coil  we  obtain  dis- 
charges in  a  single  direction  only,  instead  of  discharges 
alternating  in  direction. 


THE  EXTRA-CURRENT.  187 

307.  The  reaction  here  referred  to  connects  itself  with 
what  is  called  the  extra-current. 

308.  When  a  current  is  sent  through  a  single  primary 
coil,  the  primary  current  excites  in  the  wire  which  carries 
it,  a  secondary  current  opposed  in  direction  to  the  primary. 
The  primary  arouses  an  antagonist  in  its  own  path,  which, 
however,  immediately  disappears. 

309.  When  the  primary  circuit  is  broken,  a  secondary 
current   of  momentary  duration,  and  having  the   same 
direction   as  the  vanishing   primary,   is   evoked  in  the 
coil. 

310.  Each  of  the  two  currents  evoked  in  the  primary 
circuit  itself,  at  the  commencement  and  at  the  cessation 
of  the  primary  current,  has  been  called  by  Faraday  an 
extra-current. 

311.  The  spark  obtained  on  breaking  the  primary  cir- 
cuit is  augmented  in  brilliancy  and  power  by  the  extra- 
current. 

312.  If  a  second  circuit  be  associated  with  the  primary ; 
if,  for  example,  two  covered  wires  are  wound  round  the 
same  reel ;  on  making  one  of  them  a  primary  circuit  we 
have  the  brilliant  spark  due  to  the  extra-current,  as  long 
as  the  ends  of  the  second  coil  remain  unconnected. 

313.  But  the  moment  they  are  connected  the  extra- 
current  in  the  primary  circuit  disappears ;  there  is  an  in- 
stant reduction  in  the  brilliancy  of  the  spark. 

314.  This  is  an  example  of  the  reaction  referred  to  in 
Note  304.     By  the  closing  of  the  secondary  circuit  the 
extra-current  is  formed  in  it  instead  of  in  the  primary  one. 
Here,  in  fact,  the  extra-current  becomes  an  ordinary  in- 
duced current ;  it  is  only  so  long  as  it  remains  in  the 
primary  circuit  that  its  distinctive  name  is  applied  to  it. 


188  NOTES  ON  ELECTRICITY. 

Influence  of  Time  on  Intensity  of  Discharge.     The 
Condenser. 

315.  The  intensity  of  the  secondary  current — its  "dis- 
charging distance,"  for  example — depends  upon  the  ra- 
pidity with  which  the  primary  is  interrupted. 

316.  I  have  already  referred  to  the  passage  of  particles 
between  the  two  severed  terminals  of  a  circuit.     By  these 
particles  the  current  may  be  kept  up  for  a  short  time  after 
the  terminals  have  been  disunited.    A  gradual  dying  away 
of  the  primary  is  the  consequence. 

317.  But  to  produce  the  maximum  secondary  intensity 
it  is  necessary  that  the  primary  should  be  extinguished  at 
once. 

318.  This  is  very  effectually  accomplished  if  the  pri- 
mary be  broken  between  the  poles  of  a  strong  magnet. 
The  secondary  spark  may  be  thus  made  to  overleap  dis- 
tances, vast  in  comparison  with  those  possible  to  it  when 
the  rupture  of  contact  occurs  far  away  from  the  magnetic 
poles. 

319.  The  magnet  quenches  immediately  the  stream  of 
particles  which  accompany  the  spark.     Thus,  instead  of 
being  spread  over  a  very  sensible   interval,  the  whole 
power  of  the  primary  is  concentrated  into  an  instant  of 
time. 

320.  This  concentration  is  announced  by  the  loudness 
of  the  report  of  the  primary  spark.     This  augmentation 
of  loudness  was  first  observed  by  Page ;  it  was  explained 
by  Eijke,  who  also  exalted  in  the  way  here  indicated  the 
discharge  of  the  secondary  coil. 

321.  The  injurious  effect  of  the  spark  produced  by  the 
rupture  of  contact  in  Ruhmkorff's  coil  is  much  diminished 
by  the  employment  of  a  condenser,  which  is  attached  to 
the  primary.     It  was  introduced  by  Fizeau. 


ELECTRIC  DISCHARG.  189 

Electric  Discharge  tJirough  Rarefied  Gases  and  Vapors. 

322.  The  eleetricity  from,  the  prime  conductor  of  an 
electrical  machine  passes  through  the  air  in  the  form  of  a 
dense  and  brilliant  spark,  which  produces  a  very  audible 
report. 

323.  When  the  discharge  passes  through  rarefied  air 
the  discharging  distance  is  augmented,  and  by  sufficiently 
rarefying  the  air  the  discharge  may  be  caused  to  pass 
silently.     It  then  fills  the  tube  through  which  it  passes 
with  a  rosy  light. 

324.  This  rosy  light  has  the  same  origin  as  that  of 
the  Aurora  Borealis  ;  it  is  due  to  the  nitrogen  of  the  air. 

325.  Every  attenuated  gas  has  its  own  characteristic 
color  when  traversed  by  the  electric  discharge.     When 
examined  by  a  prism  the  color  resolves  itself  into  distinct 
bands ;  the  nature  of  the  gas  may,  indeed,  be  inferred  from, 
the  analysis  of  its  spectrum. 

326.  The  discharge  of  the  induction  coil  through  at- 
tenuated media  produces  luminous  effects  similar  to  those 
produced  by  the  electric  machine. 

327.  The  tubes  containing  the  attenuated  gases  or  va- 
pors are  usually  called  vacuum  tubes.     Through  the  tubes 
pass  platinum  wires  which  are  fused  into  the  glass,  and 
between  which  the  discharge  passes. 

328.  Such  tubes  are  produced  in  great  perfection  by 
Geissler,  of  Bonn,  and  are  sometimes  called  Geissler's 
tubes. 

329.  Under  certain  circumstances,  the  luminous  dis- 
charge is  composed  of  distinct  luminous  strata  separated 
from  each  other  by  dark  intervals  transverse  to  the  direc- 
tion of  the  discharge.     These  strata  were  first  observed 
by  Grove ;  they  were  observed  independently  and  finely 
developed  by  Ruhmkorff. 


190  NOTES   ON   ELECTRICITY. 

330.  The  luminous  strata  were  believed  to  arise  from 
the  intermittent  action  of  the  contact-breaker  of  the  in- 
duction coil ;  but  Gassiot  produced  them  both  with  the 
electric  machine,  and  with  his  battery  of  3,500  cells,  where 
no  contact-breaker  is  employed. 

331.  Every   single    discharge   of   the   induction   coil 
through  a  properly-chosen  medium  resolves  itself  into  a 
series  of  pulses,  which  declare  themselves  as  a  stratified 
discharge.      Under  similar  circumstances  the  discharge 
from  the  voltaic  battery  also  is  resolved  into  a  series  of 
pulses  which  are  declared  by  their  stratifications. 

Action  of  Magnets  on  the  Luminous  Discharge. 

332.  The  luminous  discharge  is  to  all  intents  and  pur- 
poses an  electric  current,  and  is  acted  on  by  a  magnet  like 
a  wire  carrying  a  current. 

333.  But  the  flexibility  of  the  luminous  current  in 
rarefied  gases  enables  the  magnet  to  act  upon  it  in  a  man- 
ner peculiarly  interesting  and  instructive. 

334.  Placing,  for  example,  a  tube  through  which  the 
luminous  discharge  is  passing  between  the  poles  of  an 
electro-magnet,  by  .exciting  the  magnet  the  stream  of 
light  may  be  either  deflected  or  wholly  extinguished. 

335.  In  the  latter  case,  by  interrupting  the  current 
passing  round  the  magnet,  or  by  lifting  the  tube  out  of 
the  magnetic  field,  the  luminous  discharge  is  restored. 

336.  In  certain  cases,  when  the  luminous  discharge 
consists  simply  of  a  feeble  glow,  the  supervention  of  the 
magnetic  force  draws   a   series   of  strongly-illuminated 
strata   from  the  positive  terminal  of  the  vacuum-tube ; 
when  the  magnetism  is  interrupted,  these  strata  retreat 
again  in  succession,  as  if  swallowed  up  by  the  positive 
pole.     A  number  of  exceedingly  beautiful  experiments  of 
this  character  has  been  made  by  Gassiot. 


MAGNETO-ELECTRIC  MACHINES.  191 

337.  It  has  been   stated  in  Note  306  that  the  dis- 
charges from  the  induction  coil  proceed  always  in  the 
same  direction ;  hence,  in  each  vacuum-tube  we  have  a 
positive  terminal   or  pole,  and  a  negative  terminal  or 
pole. 

338.  When  the  light  surrounding  the  negative  ter- 
minal is  subjected  to  a  magnet,  it  ranges  itself  exactly 
along  the  lines  of  magnetic  force ;  the  light  at  the  posi- 
tive terminal  shows  no  such  action.    This  discovery  is  due 
to  Plticker. 

Magneto-electric  Machines.    Saxton^s  Machine.   Siemens* 's 
Armature. 

339.  Faraday's  discovery  of  Magneto-electricity  was 
announced  in  1831.     In  1833  a  machine  was  constructed 
by  Saxton  for  the  more  copious  development  of  magneto- 
electric  currents. 

340.  In  it  copper-wire  coils,  within  which  were  placed 
cores  of  iron,  were  caused  to  rotate  before  the  poles  of  a 
powerful  magnet. 

341.  On  the  approach  of  a  coil  to  one  of  the  poles  of 
the  magnet,  a  powerful  current,  whose  direction  depended 
on  the  nature  of  the  pole,  was  induced  in  the  coil.     When 
the  coil  retreated  from  the  magnetic  pole,  a  current  in  the 
opposite  direction  was  induced.     This  production  of  op- 
posite currents  by  approach  and  withdrawal  has  been 
already  referred  to  in  Notes  283,  284. 

342.  By  means  of  an  instrument  called  a  commutator, 
which  reversed  one  of  the  induced  currents  at  the  proper 
moment,  the  opposite  currents  were  caused  to  flow  in  the 
same  direction. 

343.  The  cores  of  soft  iron  and  their  associated  coils 
constitute  what  is  called  an  armature.     In  Saxton's  arma- 
ture the  coils  were  wound  transversely  to  the  iron  cores. 


192  NOTES  ON  ELECTRICITY. 

344.  But  by  winding  his  coils  longitudinally,  or  parallel 
to  the  axis  of  the  core,  and  placing  the  armature  so  formed 
between  the  poles  of  a  series  of  horseshoe  magnets,  Siemens 
obtained  magneto-electric  currents  much  more  powerful 
than  those  of  Saxton. 

Wilde's  Machine. 

Things  were  in  this  state  when,  in  1866,  Wilde  made 
an  important  addition  to  our  knowledge  of  magneto- 
electricity. 

345.  He  conducted  the  current  obtained  by  means  of 
Siemens's  armature  round  an  electro-magnet,  and  found 
that  the  magnetism  thus  excited  was  far  greater  than 
that  of  the  entire  series  of  steel  magnets  employed  to 
generate  the  magneto-electric  current. 

346.  Thus,  in  one  case,  he  found  that  whereas  the 
series  of  permanent  magnets  taken  collectively  was  com- 
petent to  support  a  weight  of  40  Ibs.  only,  the  electro- 
magnet which  they  excited  sustained  a  weight  of  1,088  Ibs. 

347.  To  produce  this  effect,  however,  it  was  necessary 
that  the  armature  of  the  magneto-electric  machine  should 
rotate  with  great  rapidity. 

348.  But  Wilde  went  farther.     Forming  his  electro- 
magnet from  a  large  plate  of  iron,  and  placing  between  its 
long  poles  a  correspondingly  long  armature,  similar  in 
shape  and  construction  to  that  of  the  magneto-electric 
machine,  he  obtained  from  this  second  armature  currents 
of  enormously  greater  power  than  those  obtainable  from 
the  first. 

349.  These  currents  could  in  their  turn  be  sent  round  a 
second  electro-magnet,  formed  from  a  larger  plate  of  iron. 
Furnished  with  a  rotating  armature,  this  second  electro- 
magnet produced  effects  previously  unknown.     Rods  of 
iron  a  quarter  of  an  inch  in  thickness  were  fused  by  the 


SIEMENS'S  AND  WHEAT-STONE'S  MACHINE.          193 

currents,  and  they  were  also  found  competent,  when  dis- 
charged between  carbon  terminals,  to  produce  a  light  of 
intolerable  brilliancy. 

Siemens'* s  and  Wheatstone^s  Machine. 

350.  The  next  great  step  in  magneto-electricity  was 
made   simultaneously  by  Dr.  Werner  Siemens   and  Sir 
Charles  Wheatstone. 

351.  Expressed  generally,  this  discovery  consists  in 
exalting,  by  means  of  its  own  action,  to  a  high  pitch  of 
intensity  an  infinitesimal  amount  of  magnetism. 

352.  Conceive  an  electro-magnetic  core  with  a  very 
small  amount  of  residual  magnetism,  which  is  never  wholly 
absent  when  iron  has  been  once  magnetized.     Let  a  sec- 
ondary coil,  with  cores  of  soft  iron,  rotate  before  the  poles 
of  such  a  magnet.     Exceedingly  feeble  induced  currents 
will  circulate  in  the  secondary  coil.     Let  these  induced 
currents,  instead  of  being  carried  away,  be  sent  round  the 
electro-magnet  which  produced  them ;  its  magnetism  will 
be  thereby  exalted.     It  is  then  in  a  condition  to  produce 
still  stronger  currents.     These  also  being  sent  round  the 
magnet,  raise  its  magnetism  still  higher  ;  a  more  copious 
production  of  induced  currents  being  the  consequence. 
Thus  by  a  series  of  interactions  between  the  electro-magnet 
and  the  secondary  helix,  each  in  turn  exalting  the  other, 
the  electro-magnet  is  raised  from  a  state  of  almost  perfect 
neutrality  to  one  of  intense  magnetization. 

353.  When  the  magnet  has  been  raised  to  this  con- 
dition, other  coils  than  those  employed  to  magnetize  it 
may  be  caused  to  rotate  before,  or  between,  its  poles ;  the 
currents  from  these  coils  may  be  carried  away  and  made 
use  of,  for  magnetization,  for  chemical  decomposition,  or 
for  the  electric  light. 

354.  The  first  magneto-electric  machine  used  to  pro- 

9 


194  NOTES  ON  ELECTEICITY. 

duce  a  light  sufficiently  intense  for  light-houses  was  con- 
structed by  Mr.  Holmes.  In  it  permanent  steel  magnets 
and  rotating  helices  were  employed.  Mr.  Holmes  has 
lately  constructed  a  very  powerful  machine  on  the  prin- 
ciple of  Siemens  and  Wheatstone. 

Induced  Currents  of  the  Ley  den-Battery. 

355.  If  a  Ley  den  jar,  or  battery,  be  discharged  through 
a  primary  spiral,  it  evokes  a  current  in  a  secondary  spiral. 
With  a  strong  charge  this  secondary  current  may  be  caused 
to  deflagrate  a  foot  of  thin  platinum  wire. 

356.  If  the  current  from  the  secondary  spiral  be  led 
round  a  third  spiral  which  faces  a  fourth ;  on  discharging 
the  battery  through  the  primary  spiral,  the  secondary  in 
the  third  spiral  acts  the  part  of  a  primary,  and  evokes  in 
the  fourth  spiral  a  tertiary  current. 

357.  With  another  pair  of  spirals  this  tertiary  current 
can  he  made  to  generate  a  current  of  the  fourth  order ; 
this  again,  with  another  pair  of  spirals,  a  current  of  the 
fifth  order.     All  these  currents  can  impart  shocks,  ignite 
gunpowder,  or  deflagrate  wires. 

For  the  investigation  of  the  Induced  Currents  of  the 
Leyden-Battery  we  are  indebted  to  Prof.  Joseph  Henry, 
Director  of  the  Smithsonian  Institution,  and  to  Prof.  Bless, 
of  Berlin. 


THE  END. 


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THE  ORIGIN  OF  SPECIES, 

By  CHARLES  DARWIN. 


A  new  American  edition  of  "  The  Origin  of  Species,"  later  than  the  latest 
English  edition,  has  just  been  published,  with  the  author's  most  recent  cor- 
rections and  additions. 

In  the  whole  history  of  the  progress  of  knowledge  there  is  no  case  so  re- 
markable of  a  system  of  doctrines,  at  first  generally  condemned  as  false  and 
absurd,  coming  into  general  acceptance  in  the  scientific  world  in  a  single 
decade.  From  the  following  statements,  the  reader  will  infer  the  estimate 
that  is  now  placed  upon  the  man  and  his  works  by  the  highest  authorities. 

"Personally  and  practically  exercised  in  zoology,  in  minute  anatomy,  in 
geology ;  a  student  of  geographical  distribution,  not  on  maps  and  in  museums 
only,  but  by  long  voyages  and  laborious  collection ;  having  largely  advanced 
each  of  these  branches  of  science,  and  having  spent  many  years  in  gathering 
and  sifting  materials  for  his  present  work,  the  store  of  accurately-registered 
facts  upon  which  the  author  of  the  '  Origin  of  Species '  is  able  to  draw  at 
will  is  prodigious."— Prof.  T.  H.  HUXLEY. 

"Far  abler  men  than  myself  may  confess  that  they  have  not  that  imtiring 
patience  in  accumulating,  and  that  wonderful  skill  in  using,  large  masses  of 
facts  of  the  most  varied  kind — that  wide  and  accurate  physiological  knowl- 
edge— that  acuteness  in  devising,  that  skill  in  carrying  out  experiments,  and 
that  admirable  style  of  composition,  at  once  clear,  persuasive,  and  judicial, 
qualities  which,  in  their  harmonious  combination,  mark  out  Mr.  Darwin  as 
the  man,  perhaps  of  all  men  now  living,  best  fitted  for  the  great  work  he 
has  undertaken  and  accomplished." — ALFRED  RUSSELL  WALLACE. 

In  Germany  these  views  are  rapidly  extending.  Prof.  GIEKIE,  a  distin- 
guished British  geologist,  attended  the  recent  Congress  of  German  Natural- 
ists and  Physicians,  at  Innspruck,  in  which  some  eight  hundred  savants 
were  present,  and  thus  writes : 

"What  specially  struck  me  was  the  universal  sway  which  the  writings 
of  Darwin  now  exercise  over  the  German  mind.  You  see  it  on  every  side,  in 
private  conversation,  in  printed  papers,  in  all  the  many  sections  into  which 
such  a  meeting  as  that  at  Innspruck  divides.  Darwin's  name  is  often  men- 
tioned, and  always  with  the  profoundest  veneration.  But  even  where  no  al- 
lusion is  specially  made  to  him,  nay,  even  more  markedly,  where  such  allusion 
is  absent,  we  see  how  thoroughly  his  doctrines  have  permeated  the  scientific 
mind,  even  in  those  departments  of  knowledge  which  might  seem  at  first 
sight  to  be  farthest  from  natural  history.  *  You  are  still  discussing  in  Eng- 
land,' said  a  German  friend  to  me,  *  whether  or  not  the  theory  of  Darwin  can 
be  true.  We  have  got  a  long  way  beyond  that  here.  His  theory  is  now  our 
common  starting-point.'  And,  so  far  as  my  experience  went,  I  found  it  tc 
be  so." 

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THE  DESCENT  OF  MAN, 


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CHAS.  DARWIN,  M,  A.,  F.  E,  S. 

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In  these  volumes  Mr.  Darwin  has  brought  forward  all  the  facts  and 
arguments  which  science  has  to  offer  in  favor  of  the  doctrine  that  man 
has  arisen  by  gradual  development  from  the  lowest  point  of  animal  life. 
He  had  originally  intended  this  work  as  a  posthumous  publication,  but 
the  extensive  acceptance  of  the  views  unfolded  in  his  book  on  the  "  Origin 
of  Species  "  induced  him  to  believe  that  the  public  were  ripe  for  the  most 
advanced  deductions  from  his  theory  of  "Natural  Selection."  Aside  from 
the  logical  purpose  which  Mr.  Darwin  had  in  view,  his  work  is  an  original 
and  fascinating  contribution  to  the  most  interesting  portion  of  natural 
history. 

From  the  London  Spectator. 

"For  our  part,  we  find  Dr.  Darwin's  vindication  of  the  origin  of  man  a  far  more 
wonderful  vindication  of  Theism  than  Paley's  '  Natural  Theology,'  though  we  do 
not  know,  so  reticent  is  his  style,  whether  or  not  he  conceives  it  himsell." 
From  the  Citizen  and  Hound  Table. 

"  Even  the  charge  of  atheism,  which  was  so  violently  urged  against  Mr.  Dar- 
win, is  now  rarely  heard,  and  theologians,  whose  orthodoxy  is  unquestioned,  have 
ventured  to  admit  that  it  is  possible  to  believe  both  in  Christianity  and  the  Dar- 
winian theory  at  the  same  time." 

From  the  Charleston  Courier. 

"No  one  can  rise  from  an  ordinarily  attentive  consideration  of  Mr.  Darwin's 
treatise,  without  being  impressed,  not  only  with  the  extent  and  depth  of  the 
knowledge  which  he  has  attained  upon  the  subject  under  treatment,  and  his  long, 
unwearied  labor  in  collecting  facts,  but  also  with  his  possession  of  qualities 
equally  rare— the  true  scientific  temper,  the  transparent  candor,  and  the  truth- 
seeking  soberness,  with  which  he  expresses  to  you  his  conclusions,  and  the  pro- 
cesses by  which  he  reaches  them. 

"  Whether  you  like  his  discourse  or  not— though  you  may  refuse  to  acquiesce 
in  his  conclusions — still  you  are  compelled  to  bear  your  witness,  that  this  man 
^as  not  been  laboring  to  find  facts  to  support  a  preconceived  theory,  but  that  the 
'heory  is  tlie  irrepressible  outgrowth  of  his  accumulated  facts.'1'' 
From  the  Evening  Bulletin. 

"  This  theory  is  now  indorsed  by  many  eminent  scientists,  who  at  first  com- 
bated it,  including  Sir  Charles  Lyell,  probably  the  most  learned  of  living  geolo- 
gists, and  even  by  a  class  of  Christian  divines  like  Dr.  McCosh,  who  think  that 
certain  theories  of  cosmogony,  like  the  nebular  hypothesis  and  the  law  of  evolu- 
tion, may  be  accepted  without  doing  violence  to  faith." 

,  to  any  address  in  the  U.  S.,  on  receipt  of  the  price. 

D.  APPLETON  &  CO.,  Publishers. 


THE  ORIGIN  OP  CIVILIZATION ; 

OR,   THE 

PRIMITIVE  CONDITION  OF  MAN. 
By  SIR   JOHN   LUBBOCK,  Bart.,  M.  P.,  F.  R.  S. 

38O    [Pages.    Illustrated. 

This  interesting  work  is  the  fruit  of  many  years'  research 
by  an  accomplished  naturalist,  and  one  well  trained  in  mod- 
ern scientific  methods,  into  the  mental,  moral,  and  social  con- 
dition of  the  lowest  savage  races.  The  want  of  a  work  of 
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being  more  and  more  applied  to  questions  of  humanity,  there 
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scribing the  conditions  of  those  tribes  of  men  who  are  lowest 
in  the  scale  of  development. 

"  This  interesting  work — for  it  is  intensely  so  in  its  aim,  scope,  and  the 
ability  of  its  author — treats  of  what  the  scientists  denominate  anthropology, 
or  the  natural  history  of  the  human  species ;  the  complete  science  of  man, 
body  and  soul,  including  sex,  temperament,  race,  civilization,  etc." — Provi- 
dence Press. 

"  A  work  which  is  most  comprehensive  in  its  aim,  and  most  admirable  in 
its  execution.  The  patience  and  judgment  bestowed  on  the  book  are  every- 
where apparent ;  the  mere  list  of  authorities  quoted  giving  evidence  of  wide 
and  impartial  reading.  The  work,  indeed,  is  not  only  a  valuable  one  on  ac- 
count of  the  opinions  it  expresses,  but  it  is  also  most  serviceable  as  a  book 
of  reference.  It  offers  an  able  and  exhaustive  table  of  a  vast  array  of  facts, 
which  no  single  student  could  well  obtain  for  himself,  and  it  has  not  been 
made  the  vehicle  for  any  special  pleading  on  the  part  of  the  author."— 
London  Athenceum. 

"  The  book  is  no  cursory  and  superficial  review ;  it  goes  to  the  very  heart 
of  the  subject,  and  embodies  the  results  of  all  the  later  investigations.  It  ia 
replete  with  curious  and  quaint  information  presented  in  a  compact,  luminous, 
and  entertaining  form." — Albany  Evening  Journal. 

"  The  treatment  of  the  subject  is  eminently  practical,  dealing  more  with 
fact  than  theory,  or  perhaps  it  will  be  more  just  to  say,  dealing  only  with 
theory  amply  sustained  by  fact." — Detroit  Free  Press. 

"  This  interesting  and  valuable  volume  illustrates,  to  some  extent,  the 
tray  in  which  the  modern  scientific  spirit  manages  to  extract  a  considerable 
treasure  from  the  chaff  and  refuse  neglected  or  thrown  aside  by  former  in 
quirers." — London  Saturday  Review. 

D.  APPLETON  &  CO.-,  Publishers. 


D.  Appleton  &  Company^  Publications. 


LAY 

ADDEESSES,    AND    KEYIEWS, 

BY  THOMAS  HENRY  HUXLEY. 
Cloth,  12mo.      380  pages.      Price,  $1.75 

THIS  is  the  latest  and  most  popular  of  the  works  of  this -in- 
trepid and  accomplished  English  thinker.  The  American  edition 
of  the  work  is  the  latest,  and  contains,  in  addition  to  the  English 
edition,  Professor  Huxley's  recent  masterly  address  on  "  Spon- 
taneous Generation,"  delivered  before  the  British  Association  for 
the  Advancement  of  Science,  of  which  he  was  president. 

The  following  is  from  an  able  article  in  the  Independent : 

The  "  Lay  Sermons,  Addresses,  and  Reviews  "  is  a  book  to  be  read 
by  every  one  who  would  keep  up  with  the  advance  of  truth — as  well  by 
those  who  are  hostile  as  those  who  are  friendly  to  his  conclusions.  In 
it,  scientific  and  philosophical  topics  are  handled  with  consummate  abil- 
ity. It  is  remarkable  for  purity  of  style  and  power  of  expression.  No- 
where, in  any  modern  work,  is  the  advancement  of  the  pursuit  of  that 
natural  knowledge,  which  is  of  vital  importance  to  bodily  and  mental 
well-being,  so  ably  handled. 

Professor  Huxley  is  undoubtedly  the  representative  scientific  man  of 
the  age.  His  reverence  for  the  right  and  devotion  to  truth  have  estab- 
lished his  leadership  of  modern  scientific  thought.  He  leads  the  beliefs 
and  aspirations  of  the  increasingly  powerful  body  of  the  younger  men  of 
science.  His  ability  for  research  is  marvellous.  'There  is  possible  no  more 
equipoise  of  judgment  than  that  to  which  he  brings  the  phenomena  of 
Nature.  Besides,  he  is  not  a  mere  scientist.  His  is  a  popularized  phi- 
losophy  ;  social  questions  have  been  treated  by  his  pen  in  a  manner  most 
masterly.  In  his  popular  addresses,  embracing  the  widest  range  of  top- 
ics, he  treads  on  ground  with  which  he  seems  thoroughly  familiar. 

There  are  those  who  hold  the  name  of  Professor  Huxley  as  synony. 
mous  with  irreverence  and  atheism.  Plato's  was  so  held,  and  Galileo's, 
and  Descartes's,  and  Newton's,  and  Faraday's.  There  can  be  no  greater 
mistake.  No  man  has  greater  reverence  for  the  Bible  than  Huxley.  No 
one  more  acquaintance  with  the  text  of  Scripture.  He  believes  there  is 
definite  government  of  the  universe  ;  that  pleasures  and  pains  are  distrib- 
uted in  accordance  with  law ;  and  that  the  certain  proportion  of  evil 
woven  up  hi  the  life  even  of  worms  will  help  the  man  "who  thinks  to  bear 
his  own  share  with  courage. 

In  the  estimate  of  Professor  Huxley's  future  influence  upon  science, 
his  youth  and  health  form  a  large  element.  He  has  just  passed  his  forty- 
fifth  year.  If  God  spare  his  life,  truth  can  hardly  fail  to  be  the  gainer 
from  a  mind  that  is  stored  with  knowledge  of  the  laws  of  the  Creator's 
operations,  and  that  has  learned  to  love  all  beauty  and  hate  ail  vileness  of 
Nature  and  art. 


SPENCERS  SYSTEM  OF  PHILOSOPHY. 

THE  PHILOSOPHY  OF  EVOLUTION, 

By  HERBERT  SPENCER. 


This  great  system  of  scientific  thought,  the  most  original  and  important  men- 
tal undertaking  of  the  age,  to  which  Mr.  Spencer  has  devoted  his  life,  is  now  well 
advanced,  the  published  volumes  being:  First  Principles,  The  Principles  of  Bi- 
ology,  two  volumes,  and  The  Principles  of  Psychology ,  vol.  i.,  which  will  be 
shortly  printed. 

This  philosophical  system  differs  from  all  its  predecessors  in  being  solidly 
based  on  the  sciences  of  observation  and  induction ;  in  representing  the  order 
and  course  of  Nature ;  in  bringing  Nature  and  man,  life,  mind,  and  society,  under 
one  great  law  of  action ;  and  in  developing  a  method  of  thought  which  may  serve 
for  practical  guidance  in  dealing  with  the  affairs  of  life.  That  Mr.  Spencer  is  the 
man  for  this  great  work  will  be  evident  from  the  following  statements : 

"  The  only  complete  and  systematic  statement  of  the  doctrine  of  Evolution 
with  which  I  am  acquainted  is  that  contained  in  Mr.  Herbert  Spencer's  '  System 
of  Philosophy ; '  a  work  which  should  be  carefully  studied  by  all  who  desire  to 
know  whither  scientific  thought  is  tending."— T.  H.  HUXLEY. 

"  Of  all  our  thinkers,  he  is  the  one  who  has  formed  to  himself  the  largest  new 
scheme  of  a  systematic  philosophy." — Prof.  MASSON. 

"  If  any  individual  influence  is  visibly  encroaching  on  Mills  in  this  country,  it 
is  his."— ma. 

"Mr.  Spencer  is  one  of  the  most  vigorous  as  well  as  boldest  thinkers  that 
English  speculation  has  yet  produced."— JOHN  SXUAKT  MILL. 

"  One  of  the  acutest  metaphysicians  of  modern  times."— Ibid. 

"  One  of  our  deepest  thinkers."— Dr.  JOSEPH  D.  HOOKEB. 

It  is  questionable  if  any  thinker  of  finer  calibre  has  appearc/l  in  our  coun- 
try."— GEORGE  HENRY  LEWES. 

"He  alone,  of  all  British  thinkers,  has  organized  a  philosophy."— Ibid. 

"  He  is  as  keen  an  analyst  as  is  known  in  the  history  of  philo&ophy ;  I  do  not 
except  either  Aristotle  or  Kant."— GEORGE  EIPLET. 

"If  we  were  to  give  our  own  judgment,  we  should  say  that,  since  Newton, 
there  has  not  in  England  been  a  philosopher  of  more  remarkable  speculative  and 
•ystematizing  talent  than  (in  spite  of  some  errors  and  some  narrowness)  Mr.  Her- 
bert Spencer."— London  Saturday  Review. 

u  We  cannot  refrain  from  offering  our  tribute  of  respect  to  one  who,  whether 
lor  Ihe  extent  of  his  positive  knowledge,  or  for  the  profundity  of  his  speculative 
insight,  has  already  achieved  a  name  second  to  none  in  the  whole  range  of  Eng- 
lish philosophy,  and  whose  works  will  worthily  sustain  the  credit  of  Englisb 
thought  in  the  present  generation."—  Westminster  Review. 


Woi  Jcs  of  Herbert  /Spencer  published  by  D.  Appleton  &  Co. 
A  NEW  SYSTEM  OF  PHILOSOPHY. 

FIRST   PRINCIPLES. 

£.  Vol.:  Large  12mo.    515  Pages.    Price  $2  50. 

CONTENTS : 
PART  FIRST. — TJie  Unknowable. 

©flaptei  ju  Religion  and  Science;  II.  Ultimate  Ecligious  Ideas;  111 
Ultimate  Scientific  Ideas;  IV.  The  Relativity  of  all  Knowledge;  V  Thi 
Reconciliation. 

PART  SECOND,— Laws  of  the  Knowable. 

I.  Laws  in  General;  II.  The  Law  of  Evolution;  III.  The  same  con- 
tinued;  IY.  The  Causes  of  Evolution;  V.  Space,  Time,  Matter,  Motion,  and 
Force ;  VL  The  Indestructibility  of  Matter ;  VII.  The  Continuity  of  Motion ; 
VIE.  The  Persistence  of  Force ;  IX.  The  Correlation  and  Equivalence  of 
Forces;  X.  The  Direction  of  Motion ;  XI.  The  Rhythm  of  Motion;  XII.  The 
Conditions  Essential  to  Evolution ;  XIII.  The  Instability  of  the  Homoge- 
neous ;  XIV.  The  Multiplication  of  Effects ;  XV.  Differentiation  «*nd  Inte- 
gration ;  XVI.  Equilibration ;  XVII.  Summary  and  Conclusion. 

In  the  first  part  of  this  work  Mr.  Spencer  defines  the  province,  limits,  and 
relations  of  religion  and  science,  and  determines  the  legitimate  scope  of 
philosophy. 

In  part  second  he  unfolds  those  fundamental  principles  which  have  been 
arrived  at  within  the  sphere  of  the  knowable ;  which  are  true  of  all  order* 
of  phenonema,  and  thus  constitute  the  foundation  of  all  philosophy.  The 
law  of  Evolution,  Mr.  Spencer  maintains  to  be  universal,  and  he  has  here 
worked  it  out  as  the  basis  of  his  system. 

These  First  Principles  are  the  foundation  of  a  system  of  Philosophy 
bolder,  more  elaborate,  and  comprehensive  perhaps,  than  any  other  which 
oat  been  hitherto  designed  hi  England. — British  Quarterly  Review. 

A  work  lofty  hi  aim  and  remarkable  in  execution, — CornJdll  Magazine. 

In  the  works  of  Herbert  Spencer  we  have  the  rudiments  of  a  positrra 
Theology,  and  an  immense  step  toward  the  perfection  of  the  science  of  Psy- 
chology.— Christian  Examiner. 

If  we  mistake  not,  in  spite  of  the  very  negative  character  of  his  own  re» 
Bolts,  he  has  foreshadowed  some  strong  arguments  for  tke  doctrine  of  a  poei- 
felre  Christian  Theology. — New  Englander. 

.As  far  as  tke  frontiers  of  knowledge,  where  the  intellect  may  go,  there  ft 
so  living  man  whose   guidance  may  more    safely  be  trusted. — 
Sfwt&lv. 


D.  APPLETON  &  CO:S  PUBLICATIONS. 
THE 

Correlation  and  Conservation  of  Forces. 

WITH  AN 

HTKODUCTION    AND    BEIEF    BIOGE APHICAL   NOTICES 
By  EDWARD  L.  YOUMANS,  M.D.     12mo,  490  pages. 

CONTENTS. 

L  By  W.  R.  GROYE.     The  Correlation  of  Physical  Forces. 
H.  By  Prof.  HELMHOLTZ.     The  Interaction  of  Natural  Forces. 
HI.  By  J.  R.  MAYER.     1.  Remarks  on  the  Forces  of  Inorganic  Nature. 

2.  On  Celestial  Dynamics. 

3.  On  the  Mechanical  Equivalent  of  Heat. 

IV.  By  Dr.  FARADAY.    Some  Thoughts  on  the  Conservation  of  Forces. 
Y.  By  Prof.  LIEBIG.    The  Connection  and  Equivalence  of  Forces. 
VI.  By  Dr.  CARPENTER.    The  Correlation  of  the  Physical  and  Vital  Forces. 

"This  work  is  a  very  welcome  addition  to  our  scientific  literature,  and  will  b« 
particularly  acceptable  to  those  who  wish  to  obtain  a  popular,  but  at  the  same  time 
precise  and  clear  view  of  what  Faraday  justly  calls  the  highest  law  in  physical  scienca, 
the  principle  of  the  conservation  of  force.  Sufficient  attention  has  not  been  paid  to  the 
publication  of  collected  monographs  or  memoirs  upon  special  subjects.  Dr.  Youmans' 
work  exhibits  the  value  of  such  collections  in  a  very  striking  manne^,  and  we  earnestly 
hope  his  excellent  example  may  be  followed  in  other  branches  of  science." — American 
Journal  of  Science. 

"It  was  a  happy  thought  which  suggested  the  publication  of  this  volume.  The 
question  is  often  asked,  and  not  so  easily  answered,  What  are  the  new  doctrines  of  the 
Correlation  and  Conservation  of  Forces?  In  this  volume  we  have  the  answer,  and 
with  the  reasons  of  its  chief  expounders ;  those  who  are  ignorant  on  that  thcine,  can 
thus  question  the  original  authorities.1' — New  Englander. 

"We  here  have  the  original  expositions  of  the  new  Philosophy  of  Forces,  accompa- 
nied by  an  excellent  exposition  of  both  the  expositions  and  the  expositors;  the  wholo 
will  be  a  rare  treat  to  the  lovers  of  advancing  scientific  thought."— Methodist 
Quarterly  Review. 

"  This  is,  perhaps,  the  most  remarkable  book  of  the  age.  We  have  hero  the  latent 
discoveries,  and  the  highest  results  of  thought  concerning  the  nature,  laws,  and  con- 
aections  of  the  forces  of  the  universe.  No  higher  or  more  sublime  problem  can  engage 
the  intellect  of  man  than  is  discussed  by  these  doctors  of  science  intent  alone  on  aniv 
tag  at  the  truth."— Detroit  Free  Press. 

'This  work  presents  a  praiseworthy  specimen  of  complete  and  faithful  authorship, 
Bad  it*  publication  at  thie  time  will  form  an  epoch  in  tha  experience  of  army  think  ing 
mlnda."—  ibune. 


Works  of  Herbert  Spencer  published  by  D.  Appleton  &  Co. 

ILLUSTRATIONS  OF  UNIVERSAL  PROGRESS, 

A  SERIES   OF  DISCUSSIONS. 

1  Vol     Large  12mo.    470  Paflrea.    Price    $2.50. 

.    '  CONTENTS : 

American  Notice  of  Spencer's  New  System  of  Philosophy. 
I.    Progress :  its  Law  and  Cause. 
II,    Manners  and  Fashion. 

III.  The  Genesis  of  Science. 

IV,  The  Physiology  of  Laughter. 

V.  The  Origin  and  Function  of  Music. 

VI.  The  Nebular  Hypothesis. 

VII.  Bain  on  the  Emotions  and  the  Will. 

VIII.  Illogical  Geology. 

IX.  The  Development  Hypothesis. 

X.  The  Social  Organism. 

XI.  Use  and  Beauty. 

XH.  The  Sources  of  Architectural  Types. 

XIII.  The  Dse  of  Anthropomorphism. 

These  Essays  constitute  a  body  of  massive  and  original  thought  upon  a 
farge  variety  of  important  topics,  and  will  be  read  with  pleasure  by  all  who 
appreciate  a  bold  and  powerful  treatment  of  fundamental  themes.  The 
general  thought  which  pervades  this  book  is  beyond  doubt  the  most  impor- 
tant that  the  human  mind  has  yet  reached. — N.  Y.  Independent. 

Those  who  have  read  the  work  on  Education,  will  remember  the  ana- 
lytic tendency  of  the  author's  mind — his  clear  perception  and  admirable  ex- 
position of  first  principles — his  wide  grasp  of  facts — his  lucid  and  vigorous 
style,  and  the  constant  and  controlling  bearing  of  the  discussion  on  practical 
results.  These  traits  characterize  all  Mr.  Spencer's  -writings,  and  mark,  in 
an  eminent  degree,  the  present  volume. — N.  Y.  Tribune. 

We  regard  the  distinguishing  feature  of  this  work  to  be  the  peculiarly 
Interesting  character  of  its  matter  to  the  general  reader.  This  is  a  great 
literary  as  well  as  philosophic  triumph.  In  the  evolution  of  a  system  of 
Philosophy  which  demands  serious  attention,  and  a  keen  exercise  of  the  in- 
tellect to  fathom  and  appreciate,  he  has  mingled  much  that  is  really  popular 
*nd  entertaining. — Rochester  Democrat. 


Works  pubUsJted  ly  2).  Appleton  <&  Co. 


HEAT, 

CONSIDERED  AS  A  MODE  OF  MOTION, 

Being  a  Course  of  Twelve  Lectures   delivered    before  th* 
Royal  Institution  of  Great  Britain. 

BY  JOHN  TYITDALL,  F.  E.  S., 

FSOFKSSOB  or  NATUBAL  PHILOSOPHY  IN  THE  BOYAL  INSTITTTTION— AUTHOX  3*  t» 
"GLACIEES  OF  THE  ALTS,"  ETC. 

"With  One  Hundred  Illustrations.      Svo,  480  pages.    Price,  $2. 


From  tne  American  Journal  of  Science.— With  all  the  skill  which  has 
made  Faraday  the  master  of  experimental  science  in  Great  Britain,  Professor  Tyndall 
enjoys  the  advantage  of  a  superior  general  culture,  and  is  thus  enabled  to  set  forth  his 
philosophy  with  all  the  graces  of  eloquence  and  the  finish  of  superior  diction.  "With  a 
simplicity,  and  absence  of  technicalities,  which  render  his  explanations  lucid  to  un- 
scientific minds,  and  at  the  same  time  a  thoroughness  and  originality  by  which  he  in- 
structs the  most  learned,  he  unfolds  all  the  modern  philosophy  of  heat  His  work  takes 
rank  at  once  as  a  classic  upon  the  subject. 

New  York  Times. — Professor  Tyndall's  course  of  lectures  on  heat  is  one  of  the 
most  beautiful  illustrations  of  a  mode  of  handling  scientific  subjects,  which  is  com- 
paratively new,  and  which  promises  the  best  results,  both  to  science  and  to  literature 
generally ;  we  mean  the  treatment  of  subjects  in  a  style  at  once  profound  and  popu- 
lar. The  title  of  Professor  Tyndall's  work  indicates  the  theory  of  heat  held  by  him, 
and  indeed  the  only  one  now  held  by  scientific  men — it  is  a  mode  of  motion. 

Boston  Journal. — He  exhibits  the  curious  and  beautiful  workings  of  nature  in 
A  most  delightful  manner.  Before  the  reader  particles  of  water  lock  themselves  or  fly 
asunder  with  a  movement  regulated  like  a  dance.  They  form  themselves  into  liquid 
flowers  with  fine  serrated  petals,  or  into  rosettes  of  frozen  gauze ;  they  bound  upward 
In  boiling  fountains,  or  creep  slowly  onward  in  stupendous  glaciers.  Flames  burst  into 
music  and  sing,  or  cease  to  sing,  as  the  experimenter  pleases,  and  metals  paint  them- 
selves upon  a  screen  in  dazzling  hues  as  the  painter  touches  his  canvas. 

New  York  Tribune. — The  most  original  and  important  contribution  that  ha> 
yet  been  made  to  tho  theory  and  literature  of  thermotics. 

Scientific  American. — The  work  is  written  in  a  charming  style,  and  Is  th« 
most  valuable  contribution  to  scientific  literature  that  has  been  published  in  many 
fears.  It  is  the  most  popular  exposition  of  the  dynamical  theory  of  heat  that,  haa  yet 
appeared.  The  old  material  theory  of  heat  may  be  said  to  be  defunct. 

Louisville  Democrat.  —This  is  one  of  the  most  delightful  scientific  works  w« 
htye  ever  met.  The  lectures  are  so  full  of  life  and  spirit  that  we  can  almost  imagine 
the  lecturer  before  us,  and  see  his  brilliant  experiments  in  every  stage  of  their  progress. 
The  theory  is  so  carefully  and  thoroughly  explained  that  no  one  can  fail  to  understand 
it.  Such  books  as  these  create  a  love  for  science. 

Independent. — Professor  Tyndall's  expositions  and  experiments  are  remarkably 
thoughtful,  ingenious,  clear,  and  convincing ;  portions  of  the  book  have  almost  tb« 
interest  of  a  romance,  so  startling  are  the  descriptions  and  elucidations. 


UNIVERSITY  OP  CALIFORNIA  LiBRARY 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
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